Dana and her 4 friends are going on a camping trip. Dana wants to see how much fruit she can share so everyone will get the same amount of fruit. There are 5 apples, 10 oranges, 5 strawberries and 10 grapes. How much will each person get?

Answers

Answer 1

I agree that the answer is 6. 30÷5=6

Related Questions

Express the confidence interval (0.070, 0.126) in the form of

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Express the confidence interval (0.070, 0.126) in the form of p-E
Solution 1
Let's find E
2E=(0.126-0.070)
E=(0.126-0.070)/2
E=0.056/2
E=0.028
Solution 2
Let's find U
u=(0.126+0.070)/2
u=0.196/2
u=0.098
Then:
CI=(u-E < p < u+E)
Replace the number according to the formula
CI=(0.098-0.028 < p < 0.098+0.028)

a proportion relationship is represented by the equation 2x=18y.If y=kx,where k is the constant of proportionlaity,then what is the value of K?
A.9
B.2
C.1/2
D.1/9

Answers

Divide by 18 and simplify.
.. 18y/18 = 2x/18
.. y = (1/9)x

selection D is appropriate

A trinket company has a warehouse that contains 50,000 trinkets. At the end of each day, a truck picks up 4,000 trinkets to deliver to the trinket store. When the warehouse drops below 15,000 trinkets, the company will begin producing more trinkets to restore the inventory. 1) Write an equation for the number of trinkets in the factory after days. 2) After how many days will the factory begin producing trinkets?

Answers

After 9 days they will begin producing new trinkets.

The expression for the number of trinkets in the company after d days would be 50000-4000d. The inequality going along with it would be:

50000-4000d<15000

We start by cancelling 50000 from both sides by subtracting:
50000-4000d<15000-50000
-4000d<-35000

Divide both sides by -4000:
-4000d/-4000 < -35000/-4000
d > 8.75

This would round up to 9 days.

A random variable x that assumes the values x1, x2, . . . , xk is called a discrete uniform random variable if its probability mass function is f(x) = 1 k for all of x1, x2, . . . , xk and 0 otherwise. find the mean and variance of x.

Answers

Recall that for a random variable [tex]X[/tex] following a discrete distribution, the expectation of [tex]X[/tex] is given by

[tex]\mathbb E[X]=\displaystyle\sum_x x\,f_X(x)[/tex]

where [tex]f_X(x)=\mathbb P(X=x)[/tex] is the PMF of [tex]X[/tex]. We have

[tex]f_X(x)=\begin{cases}\dfrac1k&\text{for }x\in\{x_1,\ldots,x_k\}\\\\0&\text{otherwise}\end{cases}[/tex]

So the expectation (mean) of the given uniformly distributed [tex]X[/tex] is

[tex]\mathbb E[X]=\displaystyle\sum_x x\,f_X(x)=\sum_{i=1}^k x_i\,f_X(x_i)=\frac1k\sum_{i=1}^k x_i[/tex]

Without any more specific information, this is all we can say about the mean.

The variance of [tex]X[/tex] is defined by

[tex]\mathbb V[X]=\mathbb E[(X-\mathbb E[X])^2]=\mathbb E[X^2]-\mathbb E[X]^2[/tex]

In computing the second moment [tex](\mathbb E[X^2])[/tex] we run into the same issue as before - we can't find a "complete" result - but we do get

[tex]\mathbb E[X^2]=\displaystyle\sum_x x^2\,f_X(x)=\frac1k\sum_{i=1}^k{x_i}^2[/tex]

and so

[tex]\mathbb V[X]=\displaystyle\frac1k\sum_{i=1}^k{x_i}^2-\left(\frac1k\sum_{i=1}^kx_i\right)^2[/tex]

We can expand [tex]\mathbb E[X]^2[/tex] a bit. Denoting the set [tex]K=\{1,2,\ldots,k\}[/tex], we can write

[tex]\displaystyle\left(\frac1k\sum_{i=1}^kx_i\right)^2=\frac1{k^2}\left(\sum_{i=1}^k{x_i}^2+\sum_{i,j\in K,\,i\neq j}x_ix_j\right)[/tex]

and so

[tex]\mathbb V[X]=\displaystyle\left(\frac1k-\frac1{k^2}\right)\sum_{i=1}^k{x_i}^2-\frac1{k^2}\sum_{i,j\in K,\,i\neq j}x_ix_j[/tex]
[tex]\mathbb V[X]=\displaystyle\frac{k-1}{k^2}\sum_{i=1}^k{x_i}^2-\frac1{k^2}\sum_{i,j\in K,\,i\neq j}x_ix_j[/tex]

but again, that's as much as we can say without any more specific information.

Final answer:

A discrete uniform random variable has values which are equally likely to occur. The mean can be calculated by summing all the values of the variable and dividing by the number of values, represented as μ = Σx/k. The variance, a measure of dispersion, can be calculated using the formula σ² = Σ(x − μ)²/k.

Explanation:

In the context of a discrete uniform random variable, the mean (μ) and variance (σ²) can be calculated using specific formulas. This is related to the nature of a discrete uniform distribution, where x assumes the values x1, x2, ..., xk, and the probability of each outcome is equally likely.

Firstly, to find the mean

you simply need to add up all the values of x and divide by the number of values (k). This could be represented as μ = Σx/k.

Secondly, the variance can be calculated using the formula σ² = Σ(x − μ)²/k. In this equation, x represents the values of the random variable, μ is the mean (which we calculated earlier), and k represents the total number of values.

The concept here is essentially determining the central tendency (mean) and dispersion (variance) of a discrete uniform random variable. This is a fundamental topic in the field of probability and statistics.

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If r = 1, s = 2, and t = 3, what value do you expect y will have?

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um the y=8???????????

A human hair was measured to be 8.0×10−4 inch thick. A cat hair was measured to be 4.0×10−1 inch thick. How much greater is the thickness of the cat hair than the human hair? Write the answer in standard form.

Answers

Human hair: 8.0 x 10-4 = 0.00080

Cat hair: 4.0 x 10-1 = 0.40

Subtracting: 0.40 - 0.00080 = 0.3992

Using rules of precision, the answer becomes 0.40

Answer:

time 4learning answer is 500

Step-by-step explanation:

In Marissa's Calculus course, attendance counts for 5% of the grade, quizzes count for 10% of the grade, exams count for 60% of the grade, and the final exam counts for 25% of the grade. Marissa had 100% average for attendance, 93% for quizzes, 86% for exams, and 85% on the final exam. Determine Marissa's course average.

Answers

Attendence counts : 5% value × 100% ( Marissa grade ) = 5%

Quizzes: 10% value × 93% ( Marissa grade )
= 9.3%

Exams : 60% value × 86% ( Marissa grade )
= 49.6%

Final Exam : 25% value × 85% ( Marissa grade)
= 21.25%

Add all the grades:
5 + 9.3 + 49.6 + 21.25 = 85.15

Marrissa's average grade is 85.15%

I hope you understood my brief explanation. And please consider marking this awnser as Branliest if you think it deserves it. Thank you :) !

Final answer:

Marissa's course average is calculated by weighting each grade by its importance and then summing. This results in an overall average grade of 87.15%.

Explanation:

To calculate Marissa's course average given the percentage weight of each grading category and her averages in each category, we multiply each of her grades by the respective weight, then add the weighted grades together.

So, the calculation would be as follows:

Attendance grade: 100% * 0.05 = 5

Quiz grade: [tex]93 * 0.10 = 9.3[/tex]

Exams grade: [tex]86 * 0.60 = 51.6[/tex]

Final exam grade: [tex]85 * 0.25 = 21.25[/tex]

Adding these up, we get [tex]5 + 9.3 + 51.6 + 21.25 = 87.15[/tex]

So, Marissa's course average is 87.15%

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Why is partitioning a directed line segment with a ratio of 1:2 not the same as finding half the length of the directed line segment

Answers

The ratio would need to be 1:1 in order to split the line in half. Think of it like having two cookies. If you split those cookies between you and your friend, then you get 1 and s/he gets the other. So the ratio of your cookie count to your friend's count is 1:1

With the ratio 1:2, you would have 1 cookie while your friend has 2 cookies. This is no longer a fair split. Things are not 50/50 anymore. You have 1/3 of the cookies while your friend has 2/3 of the cookies. Your friend would have twice as much.

So that applies to the segment lengths as well. The line segment would be split up into two parts A and B. Part A is the smaller segment that is half as long as part B. Or put another way, part B is twice as long as part A

Answer:

Sample response: A ratio of 1:2 means that there are 3 parts in total. One part will be before the desired point, and 2 parts will be after the desired point. This is the same as finding the point that is 1/3 the length. Half the length of the segment would mean there would only be two pieces, each of equal size.

Step-by-step explanation:

ABCD and JKLM are similar rectangles. What is the perimeter of JKLM?

21 m

22 m

24 m

28 m

Answers

SCale factor is ML/DC = 6/4 = 3/2

So multiply AD by 3/2 to find the length of JM . The length would be 3*3/2=9/2

Next find the perimeter of JKML. It would be 2(9/2+6)=21

Answer:

Step-by-step explanation:

The owner of a bike shop sells unicycle and bicycles and keeps inventory by counting seats and wheels. One day she counts 20 seats and 28 wheels. The equation representing the total number of seats is u+b=20 where u is the number of unicycles and b is the number of bicycles. Select the equation representing the number of wheels.

Answers

A unicycle has 1 wheel. u unicycles have u wheels.

A bicycle has 2 wheels. b bicycles have 2b wheels.

In u unicycles and b bicycles, there are a total of
u + 2b wheels.

We are told there are 28 wheels, so u + 2b must equal 28.

The answer is choice C. u + 2b = 28

The equation u+2b=28 represents the number of wheels, which is correct option(C).

What is equation?

Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.

The owner of a bike shop sells unicycles and bicycles and keeps inventory by counting seats and wheels. One day, she counts 20 seats and 28 wheels.

u is the number of unicycles and b is the number of bicycles.

There are total 20 seats

⇒ u+b=20

unicycle has 1 wheel and bicycle has 2 and total there are 28 wheels

⇒ u+2b=28

Hence, this equation represents the number of wheels.

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What is the equation of the line that is parallel to the line y = x + 4 and passes through the point (6, 5)?

y = x + 3
y = x + 7
y = 3x – 13
y = 3x + 5

Answers

Answer:

Step-by-step explanation:

Final answer:

The equation of the line parallel to y = x + 4 passing through the point (6, 5) is y = x - 1, which has the same slope as the given line but a different y-intercept, determined by the given point.

Explanation:

The question asks for the equation of a line that is parallel to y = x + 4 and passes through the point (6, 5). Since the line we are looking for must be parallel, it will have the same slope as the given line, which in this case is 1 (since the coefficient of x is 1 in the given equation). The general form of the line we're looking for is y = x + b, where b is the y-intercept. To find the specific equation, we substitute the point (6, 5) into the equation to solve for b:

5 = (1)(6) + b
5 = 6 + b
b = 5 - 6
b = -1

Thus, the equation of the line that meets the conditions is y = x - 1, which is not represented in the options given. Since none of the options match, it's possible that there might have been a mistake in the options provided or an error in the transmission of the question. However, based on the information given, this is the correct equation for the line parallel to y = x + 4 that passes through (6, 5).

A tee box is 48 feet above its fairway.

Answers

0 = -16t ^ 2 + 32t + 48
Part A:
Factoring we have:
0 = -16 (t ^ 2 - 2t + -3)
0 = (t ^ 2 - 2t + -3)
0 = (t + 1) * (t-3)
t> 0
t-3 = 0
t = 3
Answer:
The ball is in the air for 3 s.

Part B:
h (t) = - 16t ^ 2 + 32t + 48
We evaluate for t = 1
h (1) = - 16 * (1) ^ 2 + 32 * (1) + 48
h (1) = 64
Answer:
The height of the ball at 1 second is:
h (1) = 64 feet

Part C:
We derive the equation and we equate to zero:
h '(t) = - 32t + 32
0 = -32t + 32
32t = 32
t = 1
h '' (t) = - 32 <0 (t = 1 is a maximum)
Answer:
Yes, The ball at its maximum height at t = 1 second.

A full bag of dog food weighs 5 1 2 pounds. How much dog food do you have if there are 3 3 4 bags in the cupboard

Answers

now, we know there are 3 and 3/4 bags in the cupboard, and each one of them weights 5 and 1/2 lbs, so the amount in the cupboard is just their product.

now, let's firstly convert the mixed fractions to "improper" and do the product after,

[tex]\bf \stackrel{mixed}{5\frac{1}{2}}\implies \cfrac{5\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{11}{2}} \\\\\\ \stackrel{mixed}{3\frac{3}{4}}\implies \cfrac{3\cdot 4+3}{2}\implies \stackrel{improper}{\cfrac{15}{4}}\\\\ -------------------------------\\\\ \cfrac{11}{2}\cdot \cfrac{15}{4}\implies \cfrac{165}{8}\implies \stackrel{lbs}{20\frac{5}{8}}[/tex]

The dog food we have if there are 3 3 4 bags in the cupboard is 20 5/8 pounds

What are proper and improper fractions and how to convert mixed fractions to simple fractions?

A fraction represents a part of a number or any number of equal parts.

There is a fraction, containing a numerator(upper value) and denominator(lower value). When the numerator is less than the denominator, the fraction is called a proper fraction, otherwise, it is called an improper fraction. A proper fraction is also called a fraction that is less than 1. And an improper fraction is ≥ 1. A mixed fraction contains a sum of whole numbers and a proper fraction.

We have been given that a full bag of dog food weighs [tex]5\dfrac{1}{2}[/tex] pounds.

First, we need to convert mixed fractions into simple fractions;

[tex]5\dfrac{1}{2}[/tex] = 11/2

Also, [tex]3\dfrac{3}{4}[/tex] = 15/4

Therefore, we know there are 3 and 3/4 bags in the cupboard, and each one of them weighs 5 and 1/2 lbs, thus the total amount in the cupboard is just their product.

[tex]5\dfrac{1}{2}[/tex] × [tex]3\dfrac{3}{4}[/tex]

11/2 × 15/4

= [tex]20\dfrac{5}{8}[/tex]

Hence, The dog food we have if there are 3 3 4 bags in the cupboard is 20 5/8 pounds.

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where do the graphs Of linear equations 2x+3y=4 and 5x+6y=7 intersect

Answers

Final answer:

The graphs of the linear equations 2x+3y=4 and 5x+6y=7 intersect at the point (2, 0).

Explanation:

The graphs of linear equations 2x+3y=4 and 5x+6y=7 intersect at a single point. To find the point of intersection, we can solve the two equations simultaneously.

Start by rearranging the equations to solve for y in terms of x:Now, set the two expressions for y equal to each other:
(-2/3)x + 4/3 = (-5/6)x + 7/6Simplify and solve for x:
-2x + 8 = -5x + 143x = 6x = 2Substitute the value of x in either original equation to find y:
2(2) + 3y = 4
4 + 3y = 4
3y = 0
y = 0

Therefore, the graphs of the two equations intersect at the point (2, 0).

A particle moves along the x-axis in such a way that its velocity at any time t > 0 is given by v(t)=3t^2-4t-4. the particl's position x(t) has a value of 1 when t=1

Answers

what's the question here?

A box contains 13 transistors, 5 of which are defective. if 5 are selected at random, find the probability that
a. all are defective.
b. none are defective.

Answers

Answer:

A. 1/1287

B. 56/1287

Step-by-step explanation:

Probability of getting all are defective transistors is 5/12.

Given that, a box contains 13 transistors, 5 of which are defective.

What is the probability?

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes

a) Probability of getting all are defective

Number of favorable outcomes = 5

Total number of outcomes = 12

Probability of getting all are defective = 5/12

b) Probability of getting none are defective

Number of favorable outcomes = 7

Total number of outcomes = 12

Probability of getting none are defective = 7/12

Therefore, probability of getting all are defective transistors is 5/12.

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Two sides of a triangle are equal in length, and the third side is 5 inches. If the perimeter is 17 inches, how long are the two equal sides?

Answers

You know the length of one side is 5in and are trying to find the length of the other two side (which, conveniently, are equal!).

Perimeter of a triangle can be found by adding up all three sides of the triangle. That means if you know the length of one side, subtracting that length from the perimeter gives you the length of the other two sides added up. So:
[tex]P = s1 + s2 + s3 [/tex]
[tex]17 = 5 + s2 + s3 [/tex]
[tex]12 = s2 + s3[/tex]

Since you know the two mystery sides are the same length, just divide 12 by 2. 12/2 = 6in. That means each one of the two equal sides is 6in long.

Rosa has 5 pounds of apples how many pies with 8 ounces of apples can Rosa make

Answers

1 pound is 16 ounces so 16*5 is 80.
80 divided by 8 is 10.
Hope this helps, sorry if wrong :)

If each pie needs 8 ounces of apple then Rosa can make 10 apple pies.
16 ounces are in 1 pound. So, [tex]16*5=80[/tex]
Next you divide [tex] \frac{80}{8} =10[/tex]
The answer is 10 pies.

Kyle bought a pair of socks for $6. Last month, his friends bought the same socks for $5. What is the percent increase in the price of the socks?

Answers

Price last month = $5
Price this month = $6

Increase in price = $6 - $5 = $1

Percentage increase = 1/5 x 100 = 20%

---------------------------------------------------
Answer: Percentage increase = 20%
---------------------------------------------------

20% will be your answer hope I helped

A pentagon has angle measures of 102°, 100°, 115° and 110°. What must the fifth angle measure?

Answers

Pentagon angles add up to 540°. So we subtract all angles above from 540° to find the fifth angle.

540 - 102- 100 - 115 - 110= 113°

ANSWER:
The fifth angle measures 113°.

Hope this helps! :)

A pentagon has angle measures of 102°, 100°, 115°, and 110°. Therefore, The fifth angle measures 113°.

What is the sum of angles in pentagon?

The sum of all the angles of Pentagon angles is 540°.

A pentagon has angle measures of 102°, 100°, 115°, and 110°.

To find the fifth angle so we subtract all angles above from 540°

102 + 100 + 115 + 110 = 540

540 - 102- 100 - 115 - 110 = 113°

Therefore, The fifth angle measures 113°.

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There are 18 students enrolled in Mr. Baker's class. Today 3 of them are absent. What is the ratio of the number of students present in class today to the total number enrolled?

Answers

Answer:

5/6

Step-by-step explanation:18 total -3 absent = 15

15 divided by 3

18 divided by 3=

5/6

The ratio for the given two numbers is 5 : 6.

What is the application ratio and proportion?

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

The total number of students are given as 18.

And, the number of students absent is 3.

Then, the number of present students is given as 18 - 3 = 15.

Now, the ratio as per the given case can be obtained as follows,

Number of students present ÷ Number of enrolled students

⇒ 15 ÷ 18

⇒ 15/18

⇒ 5 : 6

Hence, the required ratio for the two numbers is 5 : 6.

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find (g o f)(x) where f(x)= x^2-2, g(x)=5x-8

Answers

[tex]\bf \begin{cases} f(x)=x^2-2\\ g(x)=5x-8\\ (g\circ f)(x)\implies g(~~f(x)~~) \end{cases} \\\\\\ g(~~f(x)~~)=5[f(x)]~-~8\implies 5[x^2-2]~-~8 \\\\\\ ~~~~~~~~~~~~~~~~~~ 5x^2-10-8\implies 5x^2-18[/tex]

The composite function (g o f)(x) of f(x) and g(x) is 5x^2-18.

We have given that,

f(x)= x^2-2, g(x)=5x-8

What is the value of (g o f)(x)?

The value of (g o f)(x)=g(f(x)

g(f(x)=5(f(x))-8

=5(x^2-2,)-8

=5x^2-10-8

=5x^2-18

Therefore the composite function of f(x) and g(x) is 5x^2-18.

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what fraction of the letters in the word MUSHROOM are not vowels? show me how you got the answer please

Answers

5/8 because their is 8 letters and there is 3 that you underlined vowels 5 of them are not a vowel

There are 8 letters in the word 'mushroom'. Out of these letters, 3 are vowels and the other 5 are consonants (not vowels). Therefore, 5/8 of the letters in the word 'mushroom' are not vowels.

A rectangular school banner has a length of 54 inches and a width of 36 inches. A sign is made that is similar to the school banner and has a length of 17 inches. What is the ratio of the area of the school banner to the area of the sign? $$

Answers

Answer:

2916/289 = 10 26/289 ≈ 10.09

Step-by-step explanation:

The ratio of areas of similar figures is the square of the scale factor. Here, the scale factor is the ratio of lengths, so is ...

k = banner/sign = 54/17

The ratio of areas is k² = (54/17)² = 2916/289 = 10 26/289 ≈ 10.09

Final answer:

The ratio of the area of the school banner to the area of the sign is approximately 3.36:1. This was calculated by first finding the areas of both the banner and the sign, and then dividing the area of the banner by the area of the sign.

Explanation:

The subject of this question falls under Mathematics, and it deals with the concept of ratio and similar figures. In this case, the figures are a school banner and a sign, both of which are rectangular in shape. The ratio of their areas can be determined by calculating the areas of both figures and then finding the ratio of the two values.

Firstly, let's calculate the area of the school banner. The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of the school banner = 54 inches (length) * 36 inches (width) = 1944 square inches.

Next, the sign's width isn't given, but because the two shapes are similar, the ratio of the banner's length to its width is equal to the ratio of the sign's length to its width. So, if we let 'w' be the width of the sign, then 54/36 = 17/w. Solving this for 'w', the width of the sign = [tex](17 * 36) / 54 = 17*2 = 34[/tex] inches. The area of the sign, then, is 17 inches (length) * 34 inches (width) = 578 square inches.

To get the ratio of the school banner's area to the sign's area, divide 1944 by 578, which equals approximately 3.36. Therefore, the ratio of the areas is 3.36:1. Meaning for every square inch of the sign, there are approximately 3.36 square inches of the school banner.

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In △DEF, DF = 17 and m∠F=32. Find DF to the nearest tenth.

Answers

FE=14.42
ED=9.01
angle D=58
hope this helps

Angle ABC is formed by two tangents intersecting outside of a circle. If minor arc AC = 110°, what is the measure of angle ABC?

Answers

If two tangents intersect at a point outsides the circle, then its angle measure is equal to one-half the difference of its intercepted arcs.

A circle has 360 degrees, so to find the measure of the major arc, subtract 110 from 360 to get 250.

ABC = 1/2(250 - 110)
ABC = 1/2(140)
ABC = 70

The measure of angle ABC is 70 degrees.

Hope this helps =)

Answer:

Step-by-step explanation:

Given that two tangents to a circle intersect at a point B outside the circle

A and C are points of contact.

By theorem on circles we have angle ABC is equal to 1/2 the difference of intercepted arcs.

Angle of minor arc =110 and hence major arc [tex]= 360-110 = 250[/tex]

Difference = [tex]250-110 =140[/tex]

Measure of angle ABC 1/2 of 140 = 70 degrees.

Nayati wants to swim 50 miles this school year. She plans to swim 1/4 mile each day. How many days will it take her to swim 50 miles. Show your work.

Answers

It will take her 200 Days.
200 x 1/4 = 50

a rectangular fish pond is 21 ft squared in area. if the owner can surround the pond with a 20 ft fence what are the dimensions of the pond

Answers

the dimensions are 41 ft

THE ANSWER IS 41 FEET

In questions 1-5, help the developer name the streets if the entrance street is y=2/3x-7, by using the patterns you discovered in the opening activity and the chart you filled in for the closing questions. All the streets that run parallel to the entrance street ( Oak Street) were given tree names, while all those that run perpendicular to the entrance street were given flower names. If it is neither parallel nor perpendicular to the main street, then the street was labeled with an animal name.
1. Street equation: y=-3/2x-2
weeping willow street
hibiscus street
oak street
Panther street

2.Street equation: y=2/3x+4
weeping willow street
hibiscus street
oak street
gray squirrel

3. Street equation: y=8/12x-7
silver maple street
hibiscus street
oak street
raccoon street

4. Street equation: y=-2/3x-16
elm street
daffodil street
oak street
panther street

5. Street Equation: y=4/6 x+5/3
elm street
camilla street
oak street
brown bear street

Answers

1.hibiscus street (perpendicular)
2.oak street (parallel)
3.raccoon street (Neither)
4.panther street (Neither)
5.oak street (parallel)

I'm not 100% sure with the names because I was getting confused but I put what type of line it was so you can check the name yourself.

Rami sold concessions during a concert. He sold bottled water for $3.50 each and bags of trail mix for $4 each. By the end of the evening, Rami sold 400 items for a total of $1,475. How many bottles of water and how many bags of trail mix did Rami sell?

Answers

price of bottled water - $3.50 each
price of bag of trail mix - $4 each
number of bottles of water sold - x
number of bags of trail mix sold - y
cost spent for bottles - 3.5x
cost spent for bags - 4y
total cost;
3.5x + 4y = 1475 ----> 1)
total number of items
x + y = 400---2)
multiply 2nd equation by 4
4x + 4y = 1600 ---> 3)
Subtract third equation from the 1st
0.5x = 125
x = 250
when x = 250
x + y = 400
250 + y = 400
y = 150
number of bottles - 250
number of bags - 150

Rami sold 250 bottles of water and 150 bags of trail mix at the concert, totaling $1,475 in sales.

To solve the problem of how many bottles of water and bags of trail mix Rami sold, we need to set up and solve a system of linear equations based on the given information.

Let's define the variables:

- [tex]$ x $[/tex] = the number of bottles of water sold

- [tex]$ y $[/tex] = the number of bags of trail mix sold

From the problem, we have two pieces of information that we can turn into equations:

1. The total number of items sold is 400.

2. The total revenue from the items sold is $1,475.

We can write these two statements as equations:

1. [tex]$ x + y = 400 $[/tex]

2. [tex]$ 3.50x + 4y = 1475 $[/tex]

We now have a system of linear equations:

[tex]\[\begin{cases}x + y = 400 \\3.50x + 4y = 1475\end{cases}\][/tex]

Step 1: Solve the first equation for [tex]$ y $[/tex]

[tex]\[y = 400 - x\][/tex]

Step 2: Substitute [tex]$ y $[/tex] in the second equation

Replace [tex]$ y $[/tex] in the second equation with [tex]$ 400 - x $[/tex]:

[tex]\[3.50x + 4(400 - x) = 1475\][/tex]

Step 3: Simplify and solve for [tex]$ x $[/tex]

Expand and simplify the equation:

[tex]\[3.50x + 1600 - 4x = 1475\][/tex]

Combine like terms:

[tex]\[3.50x - 4x + 1600 = 1475\][/tex]

[tex]\[-0.50x + 1600 = 1475\][/tex]

Subtract 1600 from both sides:

[tex]\[-0.50x = 1475 - 1600\][/tex]

[tex]\[-0.50x = -125\][/tex]

Divide both sides by -0.50:

[tex]\[x = \frac{-125}{-0.50} = 250\][/tex]

So, Rami sold 250 bottles of water.

Step 4: Find [tex]$ y $[/tex] using the value of [tex]$ x $[/tex]

Substitute [tex]$ x = 250 $[/tex] back into the first equation:

[tex]\[y = 400 - 250 = 150\][/tex]

So, Rami sold 150 bags of trail mix.

Conclusion

Rami sold:

- 250 bottles of water

- 150 bags of trail mix

To verify, we check the total revenue:

[tex]\[3.50 \times 250 + 4 \times 150 = 875 + 600 = 1475\][/tex]

The numbers match the given total revenue, confirming our solution is correct.

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