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.

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

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2