Question

How many pounds of candy that sells for $1.25 per Ib must be mixed with candy that sells for $0.75 per lb to obtain 20 lb of a mixture that should sell for $1.20 per lb?

Answer 1

You need 18 pounds of candy

Answer 2

Let x be the number of pounds of candy that sells for $1.25 per lb that we need to mix, and let y be the number of pounds of candy that sells for $0.75 per lb. We can set up a system of equations to represent the problem:

x + y = 20 (we need a total of 20 pounds of candy in the mixture)

1.25x + 0.75y = 1.20(20) (the value of the mixture should be $1.20 per lb)

Simplifying the second equation, we get:

1.25x + 0.75y = 24

Multiplying the first equation by 0.75 and subtracting it from the second equation, we can eliminate y:

1.25x + 0.75y = 24

0.75x + 0.75y = 15

0.5x = 9

Dividing both sides by 0.5, we get:

x = 18

Therefore, we need 18 pounds of candy that sells for $1.25 per lb and 2 pounds of candy that sells for $0.75 per lb to make a 20-pound mixture that sells for $1.20 per lb.