Question

How much caramel candies at $1.16 a pound should be mixed with lollipops worth 86¢ a pound in order to obtain a mixture of 60 pounds of candy worth a dollar a pound?

Answer 1

28 pounds of caramel candies

32 pounds of lollipops.

Explanation:

Let x represent pounds of caramel candies and y represent pounds of lollipops.

We are told that the mixture contains 60 pounds of both. We can represent this information in an equation as:

`x+y=60...(1)`

We have been given that caramel candies costs $1.16 per pound, so cost of x pounds would be
`1.16x`.

Each pound of lollipop worth 86¢ ($0.86), so cost of y pounds would be
`0.86y`.

We are asked to obtain a mixture of 60 pounds of candy worth a dollar a pound. We can represent this information in an equation as:

`1.16x+0.86y=60(1)...(2)`

From equation (1), we will get:

`y=60-x`

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

`1.16x+0.86(60-x)=60`

`1.16x+51.6-0.86x=60`

`0.30x+51.6=60`

`0.30x+51.6-51.6=60-51.6`

`0.30x=8.4`

`(0.30x)/(0.30)=(8.4)/(0.30)`

`x=28`

Therefore, 28 pounds of caramel candies at $1.16 a pound should be mixed with lollipops.

Upon substituting
`x=28` in equation (1), we will get:

`28+y=60`

`28-28+y=60-28`

`y=32`

Therefore, 32 pounds of lollipops should be mixed to obtain the required mixture.