Question

A mixture of 30 pounds of candy sells for $1.10 a pound. The mixture consists of chocolates worth $1.50 a pound and chocolates worth 90¢ a pound. How many pounds of the $1.50 chocolate were used to make the mixture?

Answer 1

Explanation:

x = pounds of cheaper chocolate

y = pounds of more expensive chocolate

30 pounds for $1.10 per pound were sold.

so, the 30 pounds cost

1.1 × 30 = $ 33.00

and then we know

x + y = 30

0.9x + 1.5y = 33

from the first equation we get

x = 30 - y

and we use that in the second equation

0.9×(30 - y) + 1.5y = 33

27 - 0.9y + 1.5y = 33

0.6y = 6

y = 10 pounds

x = 30 - y = 30 - 10 = 20 pounds

anyway, 10 pounds of the $1.50 chocolate was used.