Question

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Find the cost of each vegetable.

Let squash be x and zucchini be y

a
x=.58 y = .68

b
x=.18 y = .21

c
x=.78 y = .26

Answer 1

Let's denote the cost of one squash as \( x \) and the cost of one zucchini as \( y \). We have the following system of equations based on the problem statement:

1. From the first statement, "the cost of 5 squash and 2 zucchini is $1.32":
\[
5x + 2y = 1.32
\]

2. From the second statement, "three squash and 1 zucchini cost $0.75":
\[
3x + y = 0.75
\]

Now, we can solve this system of equations.

### Step 1: Solve the second equation for \( y \)
From the second equation:
\[
y = 0.75 - 3x
\]

### Step 2: Substitute \( y \) into the first equation
Substituting \( y \) into the first equation:
\[
5x + 2(0.75 - 3x) = 1.32
\]

### Step 3: Simplify the equation
Distributing the 2:
\[
5x + 1.5 - 6x = 1.32
\]
Combining like terms:
\[
-x + 1.5 = 1.32
\]

### Step 4: Solve for \( x \)
Subtracting 1.5 from both sides:
\[
-x = 1.32 - 1.5
\]
\[
-x = -0.18
\]
Multiplying by -1:
\[
x = 0.18
\]

### Step 5: Substitute \( x \) back to find \( y \)
Now substitute \( x = 0.18 \) back into the equation for \( y \):
\[
y = 0.75 - 3(0.18)
\]
Calculating:
\[
y = 0.75 - 0.54 = 0.21
\]

### Result
Thus, the cost of each vegetable is:
- Squash \( x = 0.18 \)
- Zucchini \( y = 0.21 \)

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