Dried cranberries cost $5.80 per pound and dried apricots cost $5.50 per pound. 15 pounds of the mixture costs $5.60 per pound. x= dried cranberries

Question

A dried fruit mixture is made from dried cranberries that cost $5.80 per pound and dried apricots that cost $5.50 per pound. Fifteen pounds of the mixture costs $5.60 per pound. Let x be the amount of dried cranberries in the mixture. 

Answer 1

Let x = the number of pounds of dried cranberries

Let y = the number of pounds of dried apricots

 

x + y = 15        x = 15 - y  (equation #1)

5.8x + 5.5y = 15(5.6)      Multiply this equation by 10

58x + 55y = 840    (equation #2)

Substitute equation #1 into equation #2

58(15 - y) + 55y = 840

870 - 58y + 55y = 840

                      -3y = -30

                           y = 10 pounds of dried apricots

 

x + 10 = 15

        x = 5 pounds of dried cranberries