Question

A coffee mixture contains beans that sell for $0.08 per pound and $0.32 per pound. If 110 pounds of beans create a

mixture that sells for $0.27 per pound, to the nearest tenth of a pound, how much of each bean is used in the
mixture? Model the scenario with an equation and solve. Use complete sentences to explain whether or not your
solution is reasonable.

Answer 1

The pounds of beans that sells for $0.08 per pound used in the mixture is 22.9 and the pounds of beans that sells for $0.32 per pound used in the mixture is 87.1

Explanation:

Let

x ----> pounds of beans that sells for $0.08 per pound

y ----> pounds of beans that sells for $0.32 per pound

we know that

`x+y=110` ----> equation A

`0.08x+0.32y=0.27(110)`

`0.08x+0.32y=29.7` ----> equation B

Solve the system by graphing

The solution of the system of equations is the intersection point both graphs

using a graphing tool

The solution is the point (22,9,87.1)

The solution is reasonable

The pounds of beans that sells for $0.08 per pound used must be less than the pounds of beans that sells for $0.32 per pound, because the unit rate of $0.27 per pound is closer to the unit rate of $0.32 per pound

see the attached figure

therefore

The pounds of beans that sells for $0.08 per pound used in the mixture is 22.9 and the pounds of beans that sells for $0.32 per pound used in the mixture is 87.1