Question

Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25. This system of equations represents the situation, where x is the cost per pound of apples, and y is the cost per pound of bananas.

Answer 1

x = 1.25

y = 0.75

Explanation:

Let $x be the cost per pound of apples

Let $y be the cost per pound of bananas

5x + 3y = 8.5 --- (1)

3x + 2y = 5.25 --- (2)

From (1),

3x + 1.8y = 5.1 --- (1a)

Subtract (1a) from (2),

(3x + 2y) - (3x + 1.8y) = 5.25 - 5.1

3x - 3x + 2y - 1.8y = 0.15

0.2y = 0.15

y = 0.15 / 0.2 = 0.75

x = [ 5.25 - 2(0.75) ] / 3 = 1.25