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

Answer:

40 pounds

Step-by-step 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 = $(70 - x)\times 19$

And we know the cost of final mixture = $70 \times 15 = 1050$

Now, putting all the value in the equation

⇒ $12x + 19 \times (70 - x) = 1050$

⇒ $1330 - 7x = 1050$

⇒ $-7x = -280$

∴ $x = 40\ pound$

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