Question

how many pounds of candy worth $12 per pound should be mixed with candy costing $19 per pound to produce a 70 pound mixture that sells for $15 per pound?

Answer 1

40 pounds

Explanation:

Given: Cost of a candy
`(c_1)`=
`\$ 12` per pound

Cost of candy
`(c_2) = \$ 19\ per\ pound`

Total amount of mixture of be produced =
`70\ pound`

Selling price of mixture =
`\$ 15 \ per\ pound`

Let´s x be the amount of
`c_1` to be mixed in the mixture.

∴ Cost of
`c_1` in the mixture = 12x

Next, Cost of
`c_2` in the mixture =
`(70 - x)* 19`

And we know the cost of final mixture =
`70 * 15 = 1050`

Now, putting all the value in the equation

⇒
`12x + 19 * (70 - x) = 1050`

⇒
`1330 - 7x = 1050`

⇒
`-7x = -280`

∴
`x = 40\ pound`

∴ 40 pounds of candy worth $12 per pound to be mixed in the mixture.