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 be the number of pounds of the $.20 beans. The cost of those beans is $.20 * x, or .20x.
Let y be the number of pounds of the $.68 beans. The cost of those beans is $ .68 * y, or .68y.
We know that 120 pounds of the mix sells for $ 0.54/pound, for a total of 120 * 0.54 = $ 64.8

x + y = 120
1.35(x) + (1.05)y = 64.8

We can rewrite the first as
x = -y + 120

Now we can substitute (-y + 120) in for (x) in the second equation, because we just proved they're equal.

.20(x) + .68(y) = 64.8
.20(-y + 120) + .68y = 64.8
-.20y + 24 + .68y = 164.8
-0.3y + 24 = 64.8
-0.38y = -24
y = 63.16