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

Answer 1

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

Answer 2

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.

Related Questions

Honi is looking at a map with a scale of 1 4 in. = 20 miles. She measured the distance from Niceville to Live Oak as 2.5 in. She found the actual distance between Niceville and Live Oak by following these steps:

Step 1: Set up a proportion 1 4 20 = 2.5 x
Step 2: Cross multiply (20)(2.5) = ( 1 4 )(x)
Step 3: Simplify 50 = 1 4 x
Step 4: Solve for x, x = 250 miles
Which step, if any, contains a mistake?
A) Step 1
B) Step 2
C) Step 3
D) Step 4

Answers

the correct question is
Honi is looking at a map with a scale of 1/4 in. = 20 miles. She measured the distance from Niceville to Live Oak as 2.5 in. She found the actual distance between Niceville and Live Oak by following these steps:

Step 1: Set up a proportion 1/4/20 = 2.5/ x
Step 2: Cross multiply (20)(2.5) = ( 1/4 )(x)
Step 3: Simplify 50 = 1/4 x
Step 4: Solve for x, x = 250 miles
Which step, if any, contains a mistake?

we have that
Step 1: Set up a proportion 1/4/20 = 2.5/ x ----------> is correct
Step 2: Cross multiply (20)(2.5) = ( 1/4 )(x) ----------> is correct
Step 3: Simplify 50 = 1/4 x --------------------------------> is correct

Step 4: Solve for x, x = 250 miles ------------> is not correct
because in the step 3 we have ----------> 50=(1/4)*x
x=50*4----------> x=200 miles

the answer the option D) Step 4

Final answer:

The mistake is in Step 4 of Honi's calculation. The correct actual distance between Niceville and Live Oak should be 200 miles instead of the 250 miles that was stated in the original steps.

Explanation:

The student's question pertains to setting up and solving a proportion to find the actual distance between two places using a map scale. The map scale given is ¼ in. = 20 miles. Honi measures a distance of 2.5 inches on the map. The steps to find the actual distance, using a proportion, should be evaluated for accuracy.

To set up the proportion correctly, we use the ratio of the map scale and compare it to the ratio of the measured distance to the actual distance (x). The correct proportion should be: (1/4 in.) / 20 miles = 2.5 in. / x miles.

Step 1 is correct, setting up the proportion based on the scale and measured distance. Step 2 involves cross-multiplying to find the relationship between the scale and the actual distance, which should yield (1/4) * x = 2.5 * 20. Step 3 should simplify this equation correctly, which would give us x = 2.5 * 20 * 4 = 200 miles. Therefore, Step 4 has a mistake because the solution provided should be 200 miles, not 250 miles as given.

A computer screen consists of small rectangular dots called pixels. Find the number of pixels on a screen that has 600 rows with 700 pixels in each row. PLEASE HELP.

Answers

It's just like finding the area of a figure. The length is 700 and the width is 600
A = LW
A = 700 * 600
A = 420,000 square units
There are 420,000 pixels on the screen.

Hope this helps =)

Answer:
Number of pixels = 420000 pixels

Explanation:
The pixels are covering the whole area of the computer screen. This means that to the number of pixels, we will simply need to get the area of the computer.
Number of pixels = area of computer screen = length * width
Number of pixels = 600*700 = 420000 pixels

Hope this helps :)

if the triangle PQR sin(P)=0.2,sin(R=)0.4 and r=22 what is length of p

Answers

we know that
the law of sines
a/sinA=b/sinB=c/sinC

then
p/sinP=r/sinR--------> p=r*sinP/sinR-------> (22*0.2)/0.4------> p=11

the answer is p=11 units

Answer:

Thank you

Step-by-step explanation:

Find the number that is smaller than 5 5/12 by as much as 2 2/13 is smaller than 6 1/6

Answers

Answer: the number is x = 1 + 21/52

Step-by-step explanation:

we have

(5 + 5/12) - x = (6 + 1/6) - (2 + 2/13)

this means that x is smaller than 5 + 5/12 by the same amount as (2 + 2/13) is smaller than (6 + 1/6)

We can solve it directly, first solve the parentheses, put the whole numbers at one side and the fractions in the other side:

5 - 6 + 2 - x = -5/12 + 1/6 - 2/13

1 - x = -5/12 + 2/12 - 2/13

1 - x = -3/12 - 2/13 = -1/4 - 2/13 = -13/(4*13) - (2*4)/(4*13) = -21/52

x = 1 + 21/52

Answer:

73/52

Step-by-step explanation:

Cereal is packaged in a box shaped like a rectangular prism with a base 7.5 by 2 inches, and a height of 10 inches. Manufacturing each box requires 10% more cardboard than the box’s surface area. How much cardboard is needed to make each box

Answers

1.10*2*(7.5*2 + 10*(7.5+2)) = 242 . . . . square inches

The total area is 2(LW +H(L +W)). You want 10% more than that, so can find it by multiplying the area by 1.10.

Find the derivative of y with respect to x. y= ((lnx)/(2+lnx))

Answers

Using the known theorem [tex]\left(\frac{f}{g}\right)'=\frac{f'g-g'f}{g^2}[/tex] you get
[tex]y'=\left(\frac{\ln x}{2+\ln x}\right) '=\frac{(\ln x)'(2+\ln x)-(2+\ln x)'\ln x}{(2+\ln x)^2}=\frac{\frac{1}{x}(2+\ln x)-\frac{1}{x}\ln x}{(2+\ln x)^2}[/tex].

Therefore, [tex]y'=\frac{\frac{2+\ln x}{x}-\frac{\ln x}{x}}{(2+\ln x)^2}=\frac{\frac{2}{x}}{(2+\ln x)^2}=\frac{2}{x(2+\ln x)^2}[/tex].

find the values of x that satisfy

Answers

Setup 2 problems
2x - 7 < 15   and    2x - 7 > -15
2x < 22                  2x > -8
x < 11                    x > -4

Or you can write it -4 < x < 11

what is the common ratio of the geometric sequence below? -96,48, -24, 12, -6,..

Answers

Hey there :)

-96, 48, -24, 12, -6

Each term is divided by - 2 or multiplied by [tex] -\frac{1}{2} [/tex]

[tex] \frac{48}{-96} [/tex] = [tex] -\frac{1}{2} [/tex]
[tex] \frac{-24}{48} [/tex] = [tex]- \frac{1}{2} [/tex]
[tex] \frac{12}{-24} [/tex] = [tex]- \frac{1}{2} [/tex]
[tex] \frac-{6}{12} [/tex] = [tex]- \frac{1}{2} [/tex]

The common ratio is -[tex] \frac{1}{2} [/tex]

The common ratio of the given geometric sequence is [tex]-\frac{1}{2}[/tex], as each term is half the value and opposite in sign of the previous term.

The common ratio of a geometric sequence can be found by dividing any term by the previous term. In the given sequence, -96, 48, -24, 12, -6,..., let's divide the second term by the first term:

Common ratio (r) = [tex]\frac{48 }{-96} = -\frac{1}{2}[/tex]

This ratio will be consistent throughout the sequence. For example, dividing the third term by the second term also gives [tex]-\frac{24 }{ 48} = -\frac{1}{2}[/tex], confirming that the common ratio is indeed [tex]-\frac{1}{2}[/tex].

which number is irrational? A.0.7 repeating B. √3 C. 4/3 D. 3.14

Answers

By definition, we have:
In mathematics, an irrational number is a number that can not be expressed as a fraction m / n, where m and n are integers and n is different from zero.
It is any real number that is not rational, and its decimal expression is neither exact nor periodic.
Therefore, the following number is irrational:
√3
Its result is:
√3 = 1.732050808
Answer:
The following number is an irrational number:
B. √3

32 15' 66" is the same as _____. Round to the nearest hundredth of a degree. Answer:

Answers

First, convert 15'66'' to degrees. Every degree is 60' and every minute (') is 60''. Thus, 15' x (1° / 60') = 0.25°and 66'' x (1' / 60'') x (1° / 60') = 0.01833°Add all the measurements in degrees including the 32° from the given. That is, 32° + 0.25° + 0.01833° = 32.268°Rounding the answer to the nearest hundredth gives us 32.27°.

Answer:

32.27

Step-by-step explanation:

Carter has 60 balloons. 4/12 of the balloons are black, and 3/12 of the balloons are white. The rest of the balloons are red. Which series of calculations shows how many red balloons Carter has?

Answers

Divide 60 by 12 and multiply that answer by 7. Take that answer and subtract it from 60, the number you have left over should be the number of red balloons you have.

Answer: 25, mark brainlist

Step-by-step explanation:

The point (5, -2) is rotated 90° about the origin. Its image is
a.(-2, 5)
b.(2, 5)
c.(-5, 2)

Answers

rotated 90° about the origin
(x,y) = (-y, x)

so (5, -2) is rotated 90° about the origin = (2, 5)

answer
b.(2, 5)

At a movie, 1/4 of the people in the theater were men, 5/8 were woman l, and the rest were children. If there were 100 more woman than children, what was the total number of people in the theater.

Answers

Let
x---------------> number of men in the theater
y---------------> number of women in the theater
z---------------> number of children in the theater
T--------------> total number of persons in the theater

we know that
T=x+y+z
x=(1/4)*T
y=(5/8)*T----------> equation 1
z=T-[(1/4)*T+(5/8)*T]-----> z=T-(7/8)*T------> z=(8*T-7*T)/8------> z=(1/8)*T
z=(1/8)*T----------> equation 2

y=100+z--------> equation 3
I substitute (1) and (2) in (3)
(5/8)*T=100+(1/8)*T------> (5/8)*T-(1/8)*T=100--------> T=200 persons

the total number of people in the theater was 200 persons
number of men in the theater------> 200*(1/4)=50 men
number of women in the theater----> 200*(5/8)=125 women
number of children in the theater----> 200*(1/8)=25 children

If carleys mows the lawn for 2 weeks Ina row and does her chores 7 weeks straight how many more weeks will she need

Answers

Well how much money is she earning? And how much does she need to have this question isn't clear enough sorry

A triangle shaped paper’s height is 18 cm and width is 10 cm. Find the hypotenuse of the paper.

Answers

The hypotenuse is 20.59. 10^2+18^2=C^2

The hypotenuse of the paper is 2√106 cm.

What is Pythagorean theorem ?

Hypotenuse ² = Height ² + Width ²

Know more about Pythagorean theorem,

The Pythagorean Theorem, also known as the Pythagoras Theorem, explains the relationship between the three sides of a right triangle. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle. Pythagorean triangles are the name given to the sides of a right triangle. Let's learn about Pythagorean theorem, formula, derivation and examples in detail.

The history of the Pythagorean theorem goes back to the ancient Babylonian and Egyptian era. The Greek mathematician Pythagoras of Samos introduced the Pythagorean theorem. Pythagoras was born in 570 BC. The Greek philosopher studied with other monks and formed a group of people; he finally stated the Pythagorean theorem. Even before Pythagoras, the ratio was shown on a Babylonian tablet 4000 years ago, but the theorem is published under the name of Pythagoras.

Here given, a triangle shaped paper’s height is 18 cm and width is 10 cm.

We want find the hypotenuse of the paper ?

Here, height of the paper = 18 cm and width of the triangle = 10 cm.

[tex] = {18}^{2} + {10}^{2} \\ = 324 + 100 \\ = 424[/tex]

So,

[tex]hypotenuse = \sqrt{424} \\ = \sqrt{2 \times 2 \times 2 \times 53} \\ = 2 \sqrt{2 \times 53} \\ = 2 \sqrt{106} \: cm[/tex]

Therefore,the hypotenuse of the paper is 2√106 cm.

Pythagoras theorem related one more question:

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Rebekah wants to read a certain number of pages each day during summer vacation. Today she reads 204 pages, which is 136% of her goal. How many pages does Rebekah want to read each day?

Answers

Rule of three
Pages %
204 → 136%
x → 100% (her goal)

x=204*100%/136%
x=150 pages

Answer: Rebeca wants to read 150 pages each day

Given that Rebekah wants to read a certain number of pages each day and today she has read a total of 204 pages which is 136% of her goal, to find the number of pages that she wants to read per day we proceed as follows:
The percentage of pages she wants to read is 100%
thus the number of pages represented by this is:
100/136×204
=150 pages

A farmer raises chickens and cows. There are 34 animals in all. The farmer counts 110 legs on these animals. How many of each animal does the farmer have?

Answers

Ccows = x
Chickens = y

x+y = 34
4x + 2y = 110 or 2x + y = 55
subtract them
x = 21

so, 21 Cows and 13 Chickens, Total = 34

check:
Cowlegs = 84
Chickenlegs = 26
Total = 110

13 chickens and 21 cows

In a right triangle a=2b+4 and all side lengths are integers. The possible values for b are 4cm, 5cm, 8cm,10cm,12cm,and 24cm. Determine the values for a,b, and c. For the right triangle, a is ______cm long, b is _________cm long, and c is __________cm long. Create a similar triangle with different side lengths. Draw and label the side lengths.

Answers

a) The values for (a, b, c) are (24 cm, 10 cm, 26 cm).

b) A similar triangle is one with sides 12 cm, 5 cm, and 13 cm.

(a) A convex, 11-sided polygon can have at most how many obtuse interior angles? (b) A convex, 11-sided polygon can have at most how many acute interior angles?
Please provide an explanation!

Answers

A) All 11 interior angles may be obtuse.
B) At most 3 interior angles may be acute.

Explanation:
A) To find the sum of the angles of a polygon, we use (n-2)(180), where n is the number of sides. We would then have (11-2)(180)=9(180)=1620. If the polygon is regular, we divide this by the number of sides; 1620/11 = 147.23. Thus all 11 angles would be obtuse in a regular 11-sided figure.

B) All interior angles of a polygon have an exterior angle that is supplementary to it. If the interior angles are acute, that means the exterior angles are obtuse. Likewise, if the interior angles are obtuse, the exterior angles would have to be acute.

The sum of the exterior angles of any polygon is 360. This means there can be no more than 3 obtuse exterior angles; since obtuse means greater than 90, if there were 4 obtuse angles, 4 angles greater than 90, the sum would be more than 360. If there can be no more than 3 obtuse exterior angles, then there can be no more than 3 acute interior angles.

Experts/ace/geniuses helpp

Answers

because the .21 is repeating the fraction is:

1 and 21/99

0.2121... = 21 / 99

So your answer is 1 21/99 = 120 / 99 answer

solve on the interval (0,pi)
1+cosθ=((sqrt3)+2)/2

Answers

[tex]\bf 1+cos(\theta )=\cfrac{\sqrt{3}+2}{2}\implies cos(\theta )=\cfrac{\sqrt{3}+2}{2}-1 \\\\\\ cos(\theta )=\cfrac{\sqrt{3}+2}{2}-\cfrac{2}{2}\implies cos(\theta )=\cfrac{\sqrt{3}\underline{+2-2}}{2}\implies cos(\theta )=\pm\cfrac{\sqrt{3}}{2} \\\\\\ cos^{-1}[cos(\theta )]=cos^{-1}\left( \pm\cfrac{\sqrt{3}}{2} \right)\implies \measuredangle \theta = \begin{cases} \frac{\pi }{6}\\\\ \frac{5\pi }{6}\\\\ \frac{7\pi }{6}\\\\ \frac{11\pi }{6} \end{cases}[/tex]

I don’t really get it please help me out!

Answers

The greatest amount of sap collected was 1 gallon. The lowest was 1/4 of a gallon. 1 gallon is 4 times as great as 1/4. So the answer is 4.

Determing wheter two ratios form a proportion

Answers

(2 3/8)/(1 1/2) = (19/8)/(3/2) = (19/8)*(2/3) = 19/12

(9 1/2)/6 = (17/2)/6 = 17/12

17/12 ≠ 19/12

The two pairs of numbers are NOT proportional.

Penélope bakes pretzels. She salts 3/8 of the pretzels. Write a fraction that is equivalent to 3/8.

Answers

An equivalent is 6/16

3/8= (2*3)/(2*8)=6/16 generally we could says that (n*3)/(n*8) for n positive integer will be a equivalent fraction of 3/8

Which of these examples is an error of addition by one?
A. 46,371 + 32,618 = 78,989
B. 38,273 + 51,425 = 89,798
C. 13,246 + 84,631 = 97,877
D. 52,634 + 25,145 = 77,779

Answers

Your answer will be B the reason is because 38,273+51,425=89698

Answer: B. 38,273 + 51,425 = 89,798

Step-by-step explanation:

Let's check all the sum by adding their corresponding places.

A. [tex]46,371 + 32,618 = 78,989[/tex]

Its correct.

B. [tex]38,273 + 51,425 =89698\neq 89,798[/tex]

Here when we add the digits on the hundredth place we get 6 not 7.

Hence, it is the example of an error of addition by one.

Its correct.

C. [tex]13,246 + 84,631 = 97,877[/tex]

Its correct.

D. [tex]52,634 + 25,145 = 77,779[/tex]

Its correct.

a step on a stairway is at least 8 inches high. Write and solve an inequality to represent the minimum number of steps between floors that are 10 feet apart

Answers

The hight of the step is

h ≥ 8 inches

If we take that in one feet we have twelve inches

The hight between floors are H=10ft = 120 inches

If we named number of steps with n, the appropriate inequality is

n ≤ 120/8 => n ≤ 15

Good luck!!!!

Answer:

If a step is "at least" 8 inches high, the minimum number of steps is theoretically 1, because that 1 step could be a 10-foot high step.

Step-by-step explanation:

Yolanda closed on a 20 year home loan for $83,000. she chooses to buy only 1 point at closing. by buying a point at her closing, yolanda reduced her monthly payment by $7.63. based on the fact that yolanda chose to buy a point at closing, what would you infer is the minimum amount of time that she will own the home? A) 6 Years B) 11 Years C) 16 Years D) 20 Years

Answers

The correct answer is B) 11 years

Minimum amount of time that Yolanda will own the home is for at least 11 years

What is Division?

A division is a process of splitting a specific amount into equal parts.

To calculate the minimum amount of time that Yolanda will own the home

We need to determine how long it will take for the monthly savings to equal the cost of the point.

One point is equal to 1% of the loan amount, so Yolanda paid $830 (1% of $83,000) at closing for the point.

To find out how many months it will take for the monthly savings to equal the cost of the point, we divide the cost of the point by the monthly savings:

$830 ÷ $7.63 = 108.77 months

Since there are 12 months in a year, 108.77 months is 11 years.

Therefore, we can infer that Yolanda will own the home for at least 11 years

To learn more on Division click:

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How many square feet of outdoor carpet will we need for this hole?

Answers

The overall rectangle is 5' by 12', so 60 ft².

The rectangular cutout is 2' by 3', so 6 ft².
The triangular cutout has a 3' base and a 4' height, so is 6 ft².

The green area is 60 ft² - 6 ft² - 6 ft² = 48 ft².

You need 48 square feet of outdoor carpet for this green in your putt-putt golf course.

Melissa had 56 pens and 37 pencils thanks. How many pencils did Melissa have?

Answers

Just by adding both of these, pens and also pencils, these actually both signify the same word, "pencils".

We do . . . .

[tex]\boxed{56+37=3}[/tex]

(93) should be your correct answer!

Help please help I need help please like pretty please btw this is on mobile

Answers

is just their difference

[tex]\bf 1-\cfrac{3}{8}\implies \cfrac{1}{1}-\cfrac{3}{8}\impliedby \textit{our LCD is 8}\implies \cfrac{8-3}{8}\implies \cfrac{5}{8}[/tex]

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