Alisha sells fruit at a farmer’s market. In one day, she sold a total of 200 pounds of apples and bananas. She sold apples for $2 per pound and bananas for $3 per pound and made $480 total. How many pounds of apples did Alisha sell?

Answer 1

Let \( x \) be the number of pounds of apples Alisha sold, and \( y \) be the number of pounds of bananas sold.

From the problem, we have the following equations based on the information provided:

1. The total weight of the fruits sold: \[ x + y = 200 \]

2. The total revenue from selling the fruits: \[ 2x + 3y = 480 \]

We can solve these equations step by step.

First, we can express \( y \) from the first equation: \[ y = 200 - x \]

Now substitute this expression for \( y \) into the second equation: \[ 2x + 3(200 - x) = 480 \]

Expanding this, we get: \[ 2x + 600 - 3x = 480 \]

Combining the \( x \) terms gives us: \[ -1x + 600 = 480 \]

Subtracting 600 from both sides results in: \[ -x = 480 - 600 \] \[ -x = -120 \]

Multiplying both sides by -1 gives: \[ x = 120 \]

Now, we substitute \( x = 120 \) back into the equation for \( y \): \[ y = 200 - 120 = 80 \]

Thus, Alisha sold:

• 120 pounds of apples
• 80 pounds of bananas

To confirm, let's check the revenue:

• Revenue from apples: \( 2 \cdot 120 = 240 \)
• Revenue from bananas: \( 3 \cdot 80 = 240 \)
• Total revenue: \( 240 + 240 = 480 \), which matches the given total.

Therefore, the number of pounds of apples Alisha sold is: \[ \boxed{120} \]