Brian and Chris went together to Target to find party favors for a birthday party they are throwing together. Brian found 4 items that cost the same amount. Chris bought 3 items that each cost $2.50 more than Brian’s items each cost. Brian and Chris both paid the same amount of money. What was the individual cost of each person's items?
(a) Write an equation. Let x represent the cost of one of Brian's items.
(b) Solve the equation. Show your work.
(c) Check your solution. Show your work.
(d) State the solution in complete sentences.
Answers
Let us assume Brian's one item cost = $ x.
Chris one item cost is $2.50 more than Brian’s items each cost.
Therefore, Chris one item cost is = $(x+2.50).
Total cost of Brian's 4 items = 4*x = 4x.
Total cost of Chris's 3 itmes = 3*(x+2.50) =3(x+2.50)
It is said that Brian and Chris both paid the same amount of money.
Therefore,
Total cost of Brian's 4 items = Total cost of Chris's 3 itmes.
a) We can setup an equation now,
4x = 3(x+2.50), where x represent the cost of one of Brian's items.b) Let us solve above equation for x.
4x = 3(x+2.50)
distributing 3 over (x+2.50), we get
4x = 3x + 7.50.
Subtracting 3x from both sides we get
4x-3x = 3x-3x =7.50.
x = 7.50.Therefore, the cost of one of Brian's items = $7.50.
Chris one item cost is $2.50 more than Brian’s items each cost.
Chris one item cost is = 7.50 +2.50 = $10.00.
c) Plugging x=7.50 in the equation we get to check the solution.
4x = 3(x+2.50)
4(7.50) = 3(7.50+2.50).
30 = 3(10.00)
30=30.
Therefore, solution x=7.50 is correct.
d) The cost of one of Brian's items is $7.50 and Chris's one item cost is $10.00.Answer:
Brians is $7.50 and chris is $10.00!
I'm sorry I don't have the math but I submitted the assignment and got a 100!
Related Questions
number 3.simplify 24cd/c
Answers
The answer is 24d because you have to simplify d_c first then you have 24c x d_c and then c cancels itself out so the answer is 24d.
Write an expression for the following a. One more than twice a number b. A number decreased by 6 c. Two-thirds of a number
Answers
a= 1+2b, b=1-6, c=2/3d. Hope this helps, I used D as a number in C you don't have to use d.
Solve 24 - 3 x = -27
Answers
-3x=-27-24(24 in right side will-24)
-3x=-51
(- on both side will cut and become + as - -=+)
3x=51
x=51/3
x=17
Thanks
Answer,
X = 17Explanation,
Step 1: Simplify both sides of the equation
24 − 3x = −27
24 + −3x = −27
−3x + 24 = −27
Step 2: Subtract 24 from both sides.
−3x + 24 − 24 = −27 − 24
−3x = −51
Step 3: Divide both sides by -3.
-3x/-3 = -51/-3
X = 17
Hope this helps :-)
sherman has 3 cats and 2 dogs.he wants to buy a toy for each of his pets. sherman has $22 to spend on pet toys.how much can he spend on each pet?write your answer as a fraction ans as an amount in dollars and cents
Answers
your correct answer is 4.27 so 4.27/22
What are fact family's for 4,9,36
Answers
4 x 9 = 36
9 x 4 = 36
36/9 = 4
36/4 = 9
Can anyone help me? I’m really stuck.
Answers
the answer for A is
7 1/2+8+6 3/4+5 1/2+6 1/4
the answer for B is
10.50 times 34/7 is equal to 51
2.
the answer for A is
9 hours, 50 minutes
the answer for B is
50.80
Find the missing term.
The roots of x² − ( ) + 34 are 5 ± 3i.
Answers
[tex]x^2-?+34=(x-(5+3i))(x-(5-3i))\\\\x^2-?+34=(x-5-3i)(x-5+3i)\\\\x^2-?+34=(x-5)^2+9\\\\x^2-?+34=x^2-10x+25+9\\\\x^2-?+34=x^2-10x+34\\\\\boxed{?=-10x}[/tex]
Answer:
Actually is 10x
Step-by-step explanation:
-10x gives you -5±3i
Four buses are available for a field trip Each bus hold 48 people write and solve. an equation that can be used to find the number of people the buses can hold.
Answers
Answer:
192
Step-by-step explanation:
4(48)=X
In order to find the amount of people per bus- 4p=192 or 192÷4=p
To find the amount of people total on the field trip- 48×4=t or [tex]\frac{t}{4}=48[/tex]
To find the number of buses used- 192÷48=b or [tex]\frac{192}{b} =48[/tex]
how to determine if its a proportional
Answers
You have to see if they are all moving up at a constant rate. You can check this by subtracting $17.40 from $21.75. It is $4.35. Then multiply $4.35 by 46. If it is not equal to $200.10, then it is not a proportional relationship. When you multiply it, you actually do get $200.1, which is equal to $200.10. So this is a proportional relationship.
Solve each component inequality and graph the solution
[tex]x > 2 and \: x - 1 \leqslant 10[/tex]
Answers
Solution: The value of x after solving both components is [tex]2<x\leq11[/tex] or [tex](2,11][/tex].
Explanation:
From the first component it is clearly noticed that the value of x is greater than 2.
Simplify the second component.
[tex]x-1\leq 10\\x\leq 11[/tex]
From the above inequality it is clearly noticed that the value of x is less than or equal to 11.
Solving both components we get [tex]2<x\leq11[/tex] and the graphical representation is shown in the figure.
The red portion shows the solutions of [tex]x>2[/tex], blue portion shows the solution of [tex]x-1\leq 10[/tex] and purple portion which combination of red and blue portion shows the solution of both inequalities.
Therefore, value of x after solving both components is [tex]2<x\leq11[/tex] or [tex](2,11][/tex].
Darian is multiplying 3/4 by 1/2
Answers
3/8 is the right answer to that question
The answer to 3/4*1/2 is
0.375
If I have two lines, will they cross? What postulate helps me answer this question?
Answers
Chloe has 26 1/4 yards of ribbon to wrap presents. She needs 3 3/4 yards for each present. How many presents can Chloe wrap?
Answers
Chloe could wrap 7 presents
Answer:
The answer above me is CORRECT
Step-by-step explanation:
I took a test with this exact answer, here is a photo with proof that I took it and this is the answer to it.
Have a nice day/night/afternoon.
Maddie...
John invests a sum of money in a retirement Account with fixed annual interest rate of 2.63% compounded continuously.After 15 years the balance reaches 1,912.41.What was the amount of initial investment
Answers
Answer: The amoun of the initial value was $1,289.
Step-by-step explanation:
1. To solve this problem you must apply the formula shown below:
[tex]A=Pe^{rt}[/tex]
Where:
- [tex]A[/tex] is the account balance ([tex]A=1,912.41[/tex]).
- [tex]P[/tex] is the principal.
- [tex]r[/tex] is the annual interest ([tex]r=0.0263[/tex]).
- [tex]t[/tex] is the time in years ([tex]t=15[/tex]).
- [tex]e[/tex]=2.7182
2. You must substitute the values into the formula and then you must solve for [tex]P[/tex], as following:
[tex]1,912.41=Pe^{(0.0263)(15)}\\1,912.41=1.48P\\P=\frac{1,912.41}{1.48}\\P=1,289[/tex]
Answer:
$ 1,289
Step-by-step explanation:
p= 1289
PLEASE HELP!! WILL MARK BRAINLIEST! NO ONE HAS BEEN ABLE TO HELP!
Answers
Answer: A
Step-by-step explanation:
Let us first observe behavior in only quadrant 1 .
On x-axis one small box represent one year.
On y-axis one small box represent one dollar.
If we see the 1 year on x-axis its corresponding value of dollar on y -axis is in mid of 4 dollars and 5 dollars.
Now if we see the 2nd year on x-axis its corresponding value of dollar on y-axis is at 6 dollars .
It concluded that after each year 0.5 dollars per pound increases.
We can see the same behavior throughout the straight line.
What equation represents this sentence?
18 less than the product of a number and 9 is 14.
Answers
18 - (9 x 14) This equation represents the sentence.
hope that helps :)
Which proportion correctly shows the equivalence of two ratios?
A. 2:3=27:18
B. 14:35=7:2
C. 4:5=32:40
D. 13:39=6:2
Answers
C. 4:5=32:40 is your answer
Treat each ratio like fractions. Note the equal sign. This means that, when each fraction is simplified, they would be the same.
4/5 = 4/5
(32/40)/(8/8) = 4/5
4/5 = 4/5
∴ (C) is your answer
~Rise Above the Ordinary, Senpai
The answer using Pythagorean theorem
Answers
h^2 = b^2+p^2
21^2 = 17^2+x^2
441 = 289 + x^2
441-289 = x^2
122 = x^2
square root of 122 is x.
therefore, x= 11.04536102.
Answer: 12.32 is the answer.
Step-by-step explanation: Using the pythagorean thereom we can solve this by using the formula A^2+B^2=C^2.
We substitute in the values,
17^2+B^2=21^2.
Now we simplify.
289+B^2=441
We subtract the 289 from both sides,
B^2=152
Now we use square root to find the answer.
12.32 is the answer.
Hope this helps!
The sum of 4 times a number and 7 is equal to 5
Answers
4x+7=5
step 1: subtract 7 from both sides
4x=-2
step 2: divide by 4 on both sides
x=-0.5
The question presents a basic algebraic problem. We translate the words into a mathematical equation, 4x + 7 = 5. After some simple manipulations (subtracting 7 from both sides and dividing the result by 4), we find that the value of x is -0.5.
Explanation:The question presents a typical example of a simple equation in Mathematics. The first step in solving this problem involves interpretation. The statement 'The sum of 4 times a number and 7 is equal to 5' can be translated into this equation: 4x + 7 = 5. To obtain the value of x, we need to isolate it on one side of the equation.
We can proceed by subtracting 7 from both sides
to achieve 4x = -2. Finally, we divide both sides of the equation by 4 to obtain x = -0.5. Thus, the number in question is -0.5.
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Can somebody help me with this I need help ASAP
Answers
Answer:
D. 300/3 = 100
Step-by-step explanation:
He needs to divide the number by 3 since he is placing 3 erasers in each bag. He needs to divide 280 by 3. 280 divided by 3 is not a choice. The closest choice is 300/3, so that is the correct answer.
Help me to answer now ineed this
Please...
Answers
[tex]\frac{\frac{y^2-4}{x^2-9}} {\frac{y-2}{x+3}}[/tex]
Let us change middle bar to division sign.
[tex]\frac{y^2-4}{x^2-9}\div \frac{y-2}{x+3}[/tex]
We now multiply with the reciprocal of the second fraction
[tex]\frac{y^2-4}{x^2-9}\times \frac{x+3}{y-2}[/tex]
We factor the first fraction using difference of two squares.
[tex]\frac{(y-2)(y+2)}{(x-3)(x+3)}\times \frac{x+3}{y-2}[/tex]
We cancel common factors.
[tex]\frac{(y+2)}{(x-3)}\times \frac{1}{1}[/tex]
This simplifies to
[tex]\frac{(y+2)}{(x-3)}[/tex]
ANSWER TO QUESTION 2
[tex]\frac{1+\frac{1}{x}} {\frac{2}{x+3}-\frac{1}{x+2}}[/tex]
We change the middle bar to the division sign
[tex](1+\frac{1}{x}) \div (\frac{2}{x+3}-\frac{1}{x+2})[/tex]
We collect LCM to obtain
[tex](\frac{x+1}{x})\div \frac{2(x+2)-1(x+3)}{(x+3)(x+2)}[/tex]
We expand and simplify to obtain,
[tex](\frac{x+1}{x})\div \frac{2x+4-x-3}{(x+3)(x+2)}[/tex]
[tex](\frac{x+1}{x})\div \frac{x+1}{(x+3)(x+2)}[/tex]
We now multiply with the reciprocal,
[tex](\frac{(x+1)}{x})\times \frac{(x+2)(x+3)}{(x+1)}[/tex]
We cancel out common factors to obtain;
[tex](\frac{1}{x})\times \frac{(x+2)(x+3)}{1}[/tex]
This simplifies to;
[tex]\frac{(x+2)(x+3)}{x}[/tex]
ANSWER TO QUESTION 3
[tex]\frac{\frac{a-b}{a+b}} {\frac{a+b}{a-b}}[/tex]
We rewrite the above expression to obtain;
[tex]\frac{a-b}{a+b}\div {\frac{a+b}{a-b}}[/tex]
We now multiply by the reciprocal,
[tex]\frac{a-b}{a+b}\times {\frac{a-b}{a+b}}[/tex]
We multiply out to get,
[tex]\frac{(a-b)^2}{(a+b)^2}[/tex]
ANSWER T0 QUESTION 4
To solve the equation,
[tex]\frac{m}{m+1} +\frac{5}{m-1} =1[/tex]
We multiply through by the LCM of [tex](m+1)(m-1)[/tex]
[tex](m+1)(m-1) \times \frac{m}{m+1} + (m+1)(m-1) \times \frac{5}{m-1} =(m+1)(m-1) \times 1[/tex]
This gives us,
[tex](m-1) \times m + (m+1) \times 5}=(m+1)(m-1)[/tex]
[tex]m^2-m+ 5m+5=m^2-1[/tex]
This simplifies to;
[tex]4m-5=-1[/tex]
[tex]4m=-1-5[/tex]
[tex]4m=-6[/tex]
[tex]\Rightarrow m=-\frac{6}{4}[/tex]
[tex]\Rightarrow m=-\frac{3}{2}[/tex]
ANSWER TO QUESTION 5
[tex]\frac{3}{5x}+ \frac{7}{2x}=1[/tex]
We multiply through with the LCM of [tex]10x[/tex]
[tex]10x \times \frac{3}{5x}+10x \times \frac{7}{2x}=10x \times1[/tex]
We simplify to get,
[tex]2 \times 3+5 \times 7=10x[/tex]
[tex]6+35=10x[/tex]
[tex]41=10x[/tex]
[tex]x=\frac{41}{10}[/tex]
[tex]x=4\frac{1}{10}[/tex]
Method 1: Simplifying the expression as it is.
[tex]\frac{\frac{3}{4}+\frac{1}{5}}{\frac{5}{8}+\frac{3}{10}}[/tex]
We find the LCM of the fractions in the numerator and those in the denominator separately.
[tex]\frac{\frac{5\times 3+ 4\times 1}{20}}{\frac{(5\times 5+3\times 4)}{40}}[/tex]
We simplify further to get,
[tex]\frac{\frac{15+ 4}{20}}{\frac{25+12}{40}}[/tex]
[tex]\frac{\frac{19}{20}}{\frac{37}{40}}[/tex]
With this method numerator divides(cancels) numerator and denominator divides (cancels) denominator
[tex]\frac{\frac{19}{1}}{\frac{37}{2}}[/tex]
Also, a denominator in the denominator multiplies a numerator in the numerator of the original fraction while a numerator in the denominator multiplies a denominator in the numerator of the original fraction.
That is;
[tex]\frac{19\times 2}{1\times 37}[/tex]
This simplifies to
[tex]\frac{38}{37}[/tex]
Method 2: Changing the middle bar to a normal division sign.
[tex](\frac{3}{4}+\frac{1}{5})\div (\frac{5}{8}+\frac{3}{10})[/tex]
We find the LCM of the fractions in the numerator and those in the denominator separately.
[tex](\frac{5\times 3+ 4\times 1}{20})\div (\frac{(5\times 5+3\times 4)}{40})[/tex]
We simplify further to get,
[tex](\frac{15+ 4}{20})\div (\frac{(25+12)}{40})[/tex]
[tex]\frac{19}{20}\div \frac{(37)}{40}[/tex]
We now multiply by the reciprocal,
[tex]\frac{19}{20}\times \frac{40}{37}[/tex]
[tex]\frac{19}{1}\times \frac{2}{37}[/tex]
[tex]\frac{38}{37}[/tex]
Mr.santino needs a total of 406 forks for his restaurant. He currently has 278 forks .15 if each set has 12 forks ,what is the minimum number of sets of forks he should buy?
Answers
he should buy 11 sets of forks, hope this helped! <3
The difference between two numbers is 15. If 8 is added to twice the greater number, the result is 4 less than 3 times the lesser number. Find the two numbers.
Answers
x - y = 15
2x + 8 = 3y - 4
Using the first equation, we can get an approximate value for x.
x = 15 + y
Now that we have a value for x, we can replace it in the second equation to find the value of y.
2(15 + y) + 8 = 3y - 4
Distributive property.
30 + 2y + 8 = 3y - 4
Combine like terms.
38 + 2y = 3y - 4
Subtract 2y from both sides.
38 = y - 4
Add 4 to both sides.
y = 42
Now that we have the value of y, we can find the value of x.
x - 42 = 15
Add 42 to both sides.
x = 57
Select all the possible solutions for 2x +7 < 3x-5
Answers
Solution :
We have to find all the possible solutions for the inequality [tex]2x+7<3x-5[/tex].
The given inequality can be solved as,
Subtracting 7 from both side , we get
[tex]2x+7-7 < 3x-5-7\\\\\Rightarrow 2x<3x-12[/tex]
Now, Subtracting 3x from both side, we get
[tex]2x-3x<3x-12-3x\\\Rightarrow -x <-12\\[/tex]
As we here we can see that both sides have similar sign, so we can cancel them out.
[tex]\Rightarrow x < 12[/tex]
Hence, the possible solution of the inequality [tex]2x+7<3x-5[/tex] is [tex]x< 12[/tex]
Find the perimeter of the parallelogram whose vertices are at (-2, 0), (0, -2), (2, 0), and (0, 2).
Answers
The perimeter of the parallelogram is 8√2.
In order to find this, we need to find the length between any of the points. You'll notice that you can create a right triangle between each set of consecutive points. As a result, you can draw the legs and use the Pythagorean Theorem. In each case, the legs will equal 2. So we find the length of the side as
Leg^2 + Leg^2 = Side^2
2^2 + 2^2 = s^2
4 + 4 = s^2
8 = s^2
√8 = s
2√2 =s
Now to find the perimeter, we multiply this length by 4.
4 * 2√2 = 8√2
The perimeter of the parallelogram with vertices at (-2, 0), (0, -2), (2, 0), and (0, 2) is 8sqrt2 units.
Explanation:In order to find the perimeter of the parallelogram with vertices at (-2, 0), (0, -2), (2, 0), and (0, 2), you firstly need to calculate the distances between the vertices to determine the lengths of the sides. The formula to find the distance between two points (x1, y1) and (x2, y2) on a graph is given by sqrt((x2-x1)² + (y2-y1)²). If we apply this formula to our coordinates, we find that the lengths of the sides of the parallelogram are sqrt((0-(-2))² + (-2-0)²)) = 2sqrt2 and sqrt((2-0)² + (0-(-2))²)) = 2sqrt2. Since a parallelogram has two pairs of equal sides, we know that the four sides will have the same length. Therefore, the perimeter of the parallelogram is 4 * 2sqrt2 = 8sqrt2 units.
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The first step in solving 5 1/2 = 2 2/7 + n/4 is to subtract 2 2/7 from both sides of the equation. true or false
Answers
Answer:
Step-by-step explanation:
the answer you are looking for is TRUE
you want to get that side so there is only the coefficient
*please mark as brainliest*
Answer: TRUE
Step-by-step explanation:
Find the value of a if x=3 is a solution to the equation x/a=7
Answers
3/a=7
a(3/a)=a(7)
3=7a or 7a=3
(7a)/7=3/7
a=3/7
Use the substitution method to solve the system of equations. Choose the correct ordered pair. 3x-y=3 y=2x+2
Answers
We have been given that
3x - y = 3 and
y = 2x + 2
Substitute y = 2x + 2 in the first equation, we get,
3x - (2x + 2) = 3
3x - 2x - 2 = 3
x - 2 = 3
x = 5
y = 2x + 2
= 2(5) + 2
= 12
Hence, the solution is (5, 12).
Answer:
B. (5,12)
Step-by-step explanation:
APEX
140 students are going in a field trip. They fill up a total of 4 buses equally. How many students are on each bus?
Answers
Your answer is 35
Hope this helps
The area of a certain state is 840,000 miles. what is this area in scientific notation
8.4 x 10^-4
84 x 10^-3
84 x 10^3
8.4 x 10^5
Plz help asap!!!!
Answers
[tex]84 \times10 \sqrt{?} [/tex]
The answer is D the last one.