Question

A store manager has 50 pounds of coffee which sells for $10 per pound. How much coffee worth $6 per pound must she mix with it so that she can sell the mixture for $8.5 per pound?

Answer 1

She needs `"30 lbs"` of coffee worth `$6` per pound.

Explanation:

You know that you have 50 lbs of coffee which sells for `$10` per pound.

Let's say that `x` represents the mass of the coffee worth `$6` per pound. When you mix this type of coffee with the original sample, you get a total mass of `50 + x` pounds.

You can charge `$8.5` per pound for the mix of coffee beans. This means that you can write one equation that helps you relate the profit you would get for each type of coffee with the profit you'd get for the mix

`underbrace(50 * 10)_(color(blue)("profit for $10 coffee")) + overbrace(x * 6)^(color(green)("profit for $6 coffee")) = underbrace((50 + x) * 8.5)_(color(orange)("profit for mix"))`

Solve this equation for `x` to get

`500 + 6x = 425 + 8.5x`

`2.5x = 75 implies x = 75/2.5 = color(green)("30 lbs")`

Therefore, if you mix 30 pounds of coffee worth `$6` per pound with 50 pounds of coffee worth `$50` per pound, you can sell the resulting mixture for `$8.5`.