Alyssa sells fruit at a farmers market and one day she sold a total of 200 lb of apples and bananas she sold apples for $2 per pound of bananas for $3 per pound and made $480 total how many pounds of apples did Alicia

Answer 1

Let \( x \) be the number of pounds of apples and \( y \) be the number of pounds of bananas. We can set up the following system of equations based on the problem statement:

1. The total weight of the apples and bananas: \[ x + y = 200 \]

2. The total revenue from selling apples and bananas: \[ 2x + 3y = 480 \]

Now, we can solve the system of equations.

From the first equation, we can express \( y \) in terms of \( x \): \[ y = 200 - x \]

Next, we substitute \( y \) in the second equation: \[ 2x + 3(200 - x) = 480 \]

Expanding that gives: \[ 2x + 600 - 3x = 480 \]

Combining like terms, we have: \[ -1x + 600 = 480 \]

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

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

So, Alyssa sold 120 pounds of apples.

To find the number of pounds of bananas, we can substitute \( x \) back into the equation for \( y \): \[ y = 200 - 120 = 80 \]

Finally, we can verify the solution:

• Total weight: \( 120 + 80 = 200 \) (correct)
• Total revenue: \( 2(120) + 3(80) = 240 + 240 = 480 \) (correct)

Thus, Alyssa sold 120 pounds of apples and 80 pounds of bananas.