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?

A. 15
B. 10
C. 12

Answer 1

B. 10

Explanation:

Let x represent pounds of chocolate worth $1.50 a pound and y represent pounds of chocolate worth 90¢ ($0.90) a pound.

We have been given that a mixture contains 30 pounds of both chocolates. We can represent this information in an equation as:

`x+y=30...(1)`

We are also told that a mixture of 30 pounds of candy sells for $1.10 a pound. We can represent this information in an equation as:

`1.50x+0.9y=30(1.10)...(2)`

From equation (1), we will get:

`y=30-x`

Upon substituting this value in equation (2), we will get:

`1.50x+0.9(30-x)=30(1.10)`

`1.50x+27-0.9x=33`

`0.60x+27-27=33-27`

`0.60x=6`

`(0.60x)/(0.60)=(6)/(0.60)`

`x=10`

Therefore, 10 pounds of the $1.50 chocolate were used to make the mixture and option B is the correct choice.