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16 October, 11:10

At a farmers' market, Frederick buys 4 pounds of apples and 14 pounds of cherries for $38.64. At the same farmers' market, Wilhelmina buys 12 pounds of apples and 7 pounds of cherries for $27.72. Determine the price per pound of apples and cherries at the farmers' market.

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  1. 16 October, 11:19
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    Price per pound of apple=$0.84

    Price per pound of cherry=$2.52

    Step-by-step explanation:

    Let apple=a

    Let cherry = c

    Fredrick

    4a+14c=38.64. (1)

    Wilhelmina

    12a+7c=27.72. (2)

    Multiply (1) by 1 and (2) by 2

    4a+14c=38.64. (3)

    24a+14c=55.44 (4)

    Subtract (3) from (4)

    20a = 16.8

    a=16.8/20

    a=0.84

    Substitute a=0.84 into equ (1)

    4a+14c=38.64

    4 (0.84) + 14c=38.64

    3.36+14c=38.64

    14c=38.64-3.36

    14c=35.28

    c=35.28/14

    c=2.52

    Price per pound of apple=$0.84

    Price per pound of cherry=$2.52

    Check

    4 (0.84) + 14 (2.52)

    3.36+35.28=38.64

    12a+7c=27.72

    12 (0.84) + 7 (2.52)

    =10.08+17.64

    =27.72
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