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.
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.
