Question

A coffee mixture has beans that sell for $0.20 a pound and beans that sell for $0.68. If 120 pounds of beans create a mixture worth $0.54 a pound, how much of each bean is used? Model the scenario then solve it. Then, in two or more sentences explain whether your solution is or is not reasonable.

Answer 1

Let $x=$ the amount of the beans of first type, $y=$ the amount of the means of second type. Then

$$x+y=120, x\geq0, y\geq0$$

The cost of the mixture

$$120\cdot0.54=64.8$$

$$0.20x+0.68y=64.8$$

Solve the system

$$x+y=120$$ $$x+3.4y=324$$

Hence

$$x+y=120$$ $$2.4y=204$$

Or

$$x=35$$ $$y=85$$

We mix 85 pounds of beans of high sort (higher cost) and 35 pounds of beans of first sort (lower cost).