A coffee mixture has beans that sell for $0.72 a pound and beans that sell for $0.52. If 110 pounds of beans create a mixture worth $0.74 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.

Question

Mathematics

Amiyah Sampson

2 October, 14:58

A coffee mixture has beans that sell for $0.72 a pound and beans that sell for $0.52. If 110 pounds of beans create a mixture worth $0.74 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.

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Eli Zimmerman · Answer 1

The price of each type of beans is such that it is impossible to create a mixture which price is higher than highest ingredient price. In this case we have one type of bean that costs $0.72 and one that cost $0.52 per pound. Even if the mixture is made purely out of first type of beans it wouldn't cost $0.74 per pound.

In general, you solve this problem using this system of equations:

x + y = 110

x*0.72 + y*0.52 = 0.74 * 100