Question

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations..
let cost of squash =x let cost of zucchini = y

a
x=.28 y = .21

b
x=.18 y = .21

c
x=.26 y = .52

Answer 1

To write a system of equations based on the cost of squash and zucchini, we can translate the given information into equations.

Let:
- \( x \) be the cost of one squash.
- \( y \) be the cost of one zucchini.

From the problem, we have the following two pieces of information:

1. The cost of 5 squash and 2 zucchini is $1.32:
\[
5x + 2y = 1.32
\]

2. The cost of 3 squash and 1 zucchini is $0.75:
\[
3x + 1y = 0.75
\]

Thus, the system of equations is:
\[
\begin{cases}
5x + 2y = 1.32 \quad \text{(1)}\\
3x + y = 0.75 \quad \text{(2)}
\end{cases}
\]

Now, we can solve this system of equations to find the values for \( x \) and \( y \).

Let's solve the second equation for \( y \):
\[
y = 0.75 - 3x
\]

Now, substitute \( y \) into the first equation:
\[
5x + 2(0.75 - 3x) = 1.32
\]
Expanding this gives:
\[
5x + 1.5 - 6x = 1.32
\]
Combine like terms:
\[
-x + 1.5 = 1.32
\]
Subtract 1.5 from both sides:
\[
-x = 1.32 - 1.5
\]
\[
-x = -0.18
\]
Multiply by -1:
\[
x = 0.18
\]

Now, substitute \( x = 0.18 \) back into the equation for \( y \):
\[
y = 0.75 - 3(0.18)
\]
\[
y = 0.75 - 0.54
\]
\[
y = 0.21
\]

Therefore, the costs are:
- Cost of squash \( (x) = 0.18 \)
- Cost of zucchini \( (y) = 0.21 \)

So the correct answer is:
**b \( x=0.18, y=0.21 \)**.