Question

Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total of $12.50. Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. The system of equations below can be used to find c, the cost of a slice of cheese pizza, and m, the cost of a slice of mushroom pizza.
3c+4m 12.50 3c+2m8.50
What is the cost of one slice of mushroom pizza?
a.$3
b.$5
c.$4
d.$2

Answer 1

We can set up the equations based on the information provided:

1. From Jack's purchase: \( 3c + 4m = 12.50 \) (Equation 1)
2. From Grace's purchase: \( 3c + 2m = 8.50 \) (Equation 2)

We will solve this system of equations to find the values of \( c \) (the cost of a slice of cheese pizza) and \( m \) (the cost of a slice of mushroom pizza).

First, we can subtract Equation 2 from Equation 1:

\[
(3c + 4m) - (3c + 2m) = 12.50 - 8.50
\]
This simplifies to:

\[
2m = 4
\]
Now, divide by 2:

\[
m = 2
\]

Now, we can find the cost of a slice of cheese pizza using \( m = 2 \). We'll substitute \( m \) back into one of the original equations—let’s use Equation 2:

\[
3c + 2(2) = 8.50
\]
\[
3c + 4 = 8.50
\]
\[
3c = 8.50 - 4
\]
\[
3c = 4.50
\]
\[
c = \frac{4.50}{3} = 1.50
\]

Now we have:
- \( c = 1.50 \) (cost of a slice of cheese pizza)
- \( m = 2 \) (cost of a slice of mushroom pizza)

Now we know that the cost of one slice of mushroom pizza is **$2**.

Therefore, the answer is:
**d.** $2