Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Question

Mrs. McCormick sometimes makes her melon salad for special events. When she made it a couple months ago, she used 7 pounds of honeydew melon and 6 pounds of watermelon, which cost her $39. Today, she used 4 pounds of honeydew melon and 6 pounds of watermelon, spending a total of $30 on the melons. Assuming that the prices of the melons haven't changed, how much does a pound of each type of melon cost?

Honeydew melon costs $
per pound and watermelon costs $
per pound.

Answer 1

Let's define variables for the prices of the melons:

• Let \( h \) be the cost per pound of honeydew melon.
• Let \( w \) be the cost per pound of watermelon.

We can set up a system of equations based on the information provided:

1. From the first scenario: \[ 7h + 6w = 39 \]

2. From the second scenario: \[ 4h + 6w = 30 \]

Now we have the system of equations:

\[ \begin{align*} (1) & \quad 7h + 6w = 39 \ (2) & \quad 4h + 6w = 30 \end{align*} \]

We can eliminate \( w \) by subtracting equation (2) from equation (1): \[ (7h + 6w) - (4h + 6w) = 39 - 30 \] This simplifies to: \[ 3h = 9 \] Dividing both sides by 3 gives us: \[ h = 3 \]

Next, we substitute \( h = 3 \) into one of the original equations to find \( w \). We'll use equation (2): \[ 4(3) + 6w = 30 \] This simplifies to: \[ 12 + 6w = 30 \] Subtracting 12 from both sides: \[ 6w = 18 \] Dividing both sides by 6 gives us: \[ w = 3 \]

Now we have the costs:

• Honeydew melon costs \( h = 3 \) dollars per pound.
• Watermelon costs \( w = 3 \) dollars per pound.

Therefore, we can fill in the blanks: Honeydew melon costs $ 3 per pound and watermelon costs $ 3 per pound.