Stephanie went to the Safeway store and bought 18 pounds of

Stephanie went to the Safeway store and bought 18 pounds of fruit consisting of apples and bananas. She paid $9 for the apples and $2.40 for the bananas. If the price per pound of the apples was 3 times that of the bananas, then how many pounds of each type of fruit did she buy?

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Solution

Let x be the pounds of apples bought, then pounds of bananas bought = 18 - x

Let the price of bananas be y dollars per pound, then price of apples = 3y dollars per pound

Cost of bananas = Number of pounds bought * price per pound = ( 18 - x ) * y = 2.4 ==> 18y - xy = 2.4 ---> (1)

Cost of apples = Number of pounds bought * price per pound = x * 3y = 9 ==> xy = 3 ---> (2)

Substituting equation (2) in equation (1)

18y - 3 = 2.4

18y = 5.4

y = 0.3

From equation (2) xy = 3

x*0.3 = 3

x = 10

Amount of bananas bought = 18 - x = 18 - 10 = 8 pounds

Amount of apples bought = x = 10 pounds