How many kilograms of each should be used?

Question

Kendall is spinning 13 kilograms of a special blended yarn. The yarn costs $38.20 per kilogram to make, and it consists of wool and acrylic fibers. The wool costs $59.90 per kilogram, whereas the acrylic costs $16.50 per kilogram. 

Answer 1

There are two unknowns, the amount of wool (W) and the amount of acrylic (A), so we need two equations.

 

W + A = 13

59.90W + 16.50A = 38.20(13)

 

W = 13 - A

59.90(13 - A) + 16.50A = 496.60

778.70 - 59.90A + 16.50A = 496.60

778.70 - 43.40A = 496.60

-43.40A = -282.10

A = 6.5

W = 13 - 6.5 = 6.5

 

So Kendall will need 6.5 kilograms of each.