Question

Quiz
Question 1 (1 point)

Listen
Ben and Joel are raising money for their class trip by selling wrapping paper. Ben raised $43.50 by selling 12 rolls of solid paper and 9 rolls of printed paper. Joel raised $51.50 by selling 8 rolls of solid paper and 15 rolls of printed paper. Find the cost of each type of wrapping paper.

Question 1 options:

$2.25 for solid and $1.50 for printed paper.


$1.75 for solid paper and $2.50 for printed paper.


$2.50 for solid paper and $1.75 for printed paper.


$1.50 for solid paper and $2.25 for printed paper.

Question 2 (1 point)

Listen
At the fast food restaurant, one hamburger and five small fries cost $8.74. If two hamburgers and three small fries cost $7.75, what is the cost of one hamburger and one fry?

Question 2 options:

$1.39 per hamburger and $1.79 per small fry.


$1.79 per hamburger and $1.39 per fry.


$1.00 per hamburger and $1.55 per small fry.


$1.55 per hamburger and $1.00 per small fry.

Question 3 (1 point)

Listen
Colton sold a total of 28 t-shirts and sweatshirts as part of a fundraiser for his football team. If t-shirts cost $12 each and sweatshirts cost $20 each and he raised a total of $424, how many of each did he sell?

Question 3 options:

26 t-shirts and 2 sweatshirts.


17 t-shirts and 11 sweatshirts.


2 t-shirts and 26 sweatshirts.


11 t-shirts and 17 sweatshirts.

Question 4 (1 point)

Listen
Katelyn has two part time jobs; tutoring and working at the grocery store. Last week, she worked a total of 15 hours. If she makes $15 per hour tutoring and $9 per hour at the grocery store and makes a total of $159, how many hours did she spend at each job?

Question 4 options:

5 hours tutoring and 10 hours at the grocery store.


11 hours tutoring and 4 hours at the grocery store.


4 hours tutoring and 11 hours at the grocery store.


10 hours tutoring and 5 hours at the grocery store.

Question 5 (1 point)

Listen
Rick bought a total of 8 pounds of steak and chicken. Id steak costs $13.50 per pound and chicken costs $3.25 per pound and he paid a total of $77.25, how many pounds of each did he buy?

Question 5 options:

3 pounds of steak and 5 pounds of chicken.


2 pounds of steak and 6 pounds of chicken.


5 pounds of steak and 3 pounds of chicken.


6 pounds of steak and 2 pounds of chicken.


0 of 5 questions saved
Listen

Answer 1

Let's solve each question step by step.

### Question 1
Ben sold 12 rolls of solid paper and 9 rolls of printed paper for a total of $43.50.
Joel sold 8 rolls of solid paper and 15 rolls of printed paper for a total of $51.50.

Let \( x \) be the cost of solid paper and \( y \) be the cost of printed paper. We can set up the following equations from the information given:

1. \( 12x + 9y = 43.50 \) (Equation 1)
2. \( 8x + 15y = 51.50 \) (Equation 2)

We can solve these simultaneous equations to find \( x \) and \( y \).

From Equation 1:
\( 12x + 9y = 43.50 \)

From Equation 2:
\( 8x + 15y = 51.50 \)

To eliminate one variable, we can multiply Equation 1 by 5 and Equation 2 by 3:

1. \( 60x + 45y = 217.50 \) (Equation 3)
2. \( 24x + 45y = 154.50 \) (Equation 4)

Subtract Equation 4 from Equation 3:
\[
(60x + 45y) - (24x + 45y) = 217.50 - 154.50
\]
\[
36x = 63
\]
\[
x = 1.75 \text{ (Cost of solid paper)}
\]

Now substitute \( x \) back into Equation 1 to find \( y \):
\[
12(1.75) + 9y = 43.50
\]
\[
21 + 9y = 43.50
\]
\[
9y = 22.50
\]
\[
y = 2.50 \text{ (Cost of printed paper)}
\]

So, the answer is:
**$1.75 for solid paper and $2.50 for printed paper.**

### Question 2
Let \( H \) be the cost of a hamburger and \( F \) be the cost of a small fry. We set up the following equations:

1. \( H + 5F = 8.74 \) (Equation 1)
2. \( 2H + 3F = 7.75 \) (Equation 2)

From Equation 1:
\[
H = 8.74 - 5F \tag{Insert into Equation 2}
\]

Putting \( H \) from Equation 1 into Equation 2:
\[
2(8.74 - 5F) + 3F = 7.75
\]
\[
17.48 - 10F + 3F = 7.75
\]
\[
17.48 - 7F = 7.75
\]
\[
-7F = -9.73
\]
\[
F = 1.39
\]

Now substitute back to find \( H \):
\[
H = 8.74 - 5(1.39) = 8.74 - 6.95 = 1.79
\]

So, the answer is:
**$1.79 per hamburger and $1.39 per fry.**

### Question 3
Let \( T \) be the number of t-shirts and \( S \) the number of sweatshirts. The equations are:

1. \( T + S = 28 \) (Equation 1)
2. \( 12T + 20S = 424 \) (Equation 2)

From Equation 1:
\[
T = 28 - S
\]

Substitute into Equation 2:
\[
12(28 - S) + 20S = 424
\]
\[
336 - 12S + 20S = 424
\]
\[
8S = 424 - 336
\]
\[
8S = 88
\]
\[
S = 11
\]

Now find \( T \):
\[
T = 28 - 11 = 17
\]

So, the answer is:
**17 t-shirts and 11 sweatshirts.**

### Question 4
Let \( x \) be the hours spent tutoring and \( y \) be the hours at the grocery store.

1. \( x + y = 15 \) (Equation 1)
2. \( 15x + 9y = 159 \) (Equation 2)

From Equation 1:
\[
x = 15 - y
\]

Substituting into Equation 2:
\[
15(15 - y) + 9y = 159
\]
\[
225 - 15y + 9y = 159
\]
\[
225 - 6y = 159
\]
\[
-6y = 159 - 225
\]
\[
-6y = -66
\]
\[
y = 11
\]

Now find \( x \):
\[
x = 15 - 11 = 4
\]

So, the answer is:
**4 hours tutoring and 11 hours at the grocery store.**

### Question 5
Let \( x \) be the pounds of steak and \( y \) be the pounds of chicken.

1. \( x + y = 8 \) (Equation 1)
2. \( 13.50x + 3.25y = 77.25 \) (Equation 2)

From Equation 1:
\[
y = 8 - x
\]

Substituting into Equation 2:
\[
13.50x + 3.25(8 - x) = 77.25
\]
\[
13.50x + 26 - 3.25x = 77.25
\]
\[
10.25x + 26 = 77.25
\]
\[
10.25x = 77.25 - 26
\]
\[
10.25x = 51.25
\]
\[
x = 5
\]

Now find \( y \):
\[
y = 8 - 5 = 3
\]

So, the answer is:
**5 pounds of steak and 3 pounds of chicken.**

### Summary of Answers:
1. **$1.75 for solid paper and $2.50 for printed paper.**
2. **$1.79 per hamburger and $1.39 per fry.**
3. **17 t-shirts and 11 sweatshirts.**
4. **4 hours tutoring and 11 hours at the grocery store.**
5. **5 pounds of steak and 3 pounds of chicken.**