mixture problem

Question

Peanuts sell for $7.00 per pound and cashews sell for $13.50 per pound. A merchant wants to sell a mixture of peanuts and cashews. How many pounds of peanuts and cashews must be used to create 21 pounds of a mixture that will sell for $8.55 per pound? Round answers off to the nearest whole number.

 

Answer 1

p + c = 21 ------> p = 21 - c

7p + 13.5c = 8.55(21)

 

7(21 - c)  + 13.5c = 179.55

147 - 7c + 13.5c = 179.55

6.5c = 32.55

c = 5

 

p = 21 - 5 = 16