farmer's market algebra

Question

At a farmers' market, Frederick buys 2 pounds of apples and 14 pounds of cherries for $38.60. At the same farmers' market, Wilhelmina buys 8 pounds of apples and 6 pounds of cherries for $24.40. Determine the price per pound of apples and cherries at the farmers' market. 

Answer 1

a = cost of apples

c = cost of cherries

2a + 14c = 38.60 and

(8a + 6c = 24.40)/ - 4 (I am dividing this equation by - 4 to keep my number low)

This becomes - 2a - 1.5c = -6.1 add this to the first equation

2a + 14.0 c = 38.6

12.5c = 32.5 divide by 13.5

c = 2.6 substitute this for c in the very first equation

2a + 14(2.6) = 38.6

2a + 36.4 = 38.6 subtract 36.4 from both sides

2a = 2.2 divide by 2

a = 1.1

Apples are $1.10/lb. and Cherries are $2.60/lb.