Question

A grocer has two kinds of candies, one selling for 90 cents a pound and the other for 40 cents a pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?

Answer 1

55 pounds of 40- cent candies, 45 pounds of candies that cost $1.40 per pound

Answer 2

If you would like to know how many pounds of each kind of candy must the grocer use to make 100 pounds worth 85 cents a pound, you can calculate this using the following steps:

Candy number 1:
c pounds = ? ... 90 cents a pound
Candy number 2:
d pounds = ? ... 40 cents a pound

c + d = 100 pounds
c = 100 pounds - d

c * 90 cents + d * 40 cents = 100 pounds * 85 cents
(100 - d) * 90 + d * 40 = 100 * 85
100 * 90 - 90 * d + d * 40 = 100 * 85
100 * 90 - 100 * 85 = 90 * d - 40 * d
500 = 50 * d
d = 500 / 50
d = 10 pounds

c = 100 pounds - d = 100 - 10 = 90 pounds

There should be 90 pounds of candy number 1 and 10 pounds of candy number 2.

90 pounds * 90 cents + 10 pounds * 40 cents = 8500 cents per 100 pounds
8500 cents / 100 pounds = 85 cents a pound