Question

PLS ANSWER 100 POINTS

A coffee mixture has beans that sell for $0.52 a pound and beans that sell for $0.28. If 130 pounds of beans create a mixture worth $0.64 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

To solve this problem, we can use a system of two equations with two unknowns. Let x be the number of pounds of beans that sell for $0.52 per pound, and let y be the number of pounds of beans that sell for $0.28 per pound. We can write:

x + y = 130 (the total weight of beans is 130 pounds)

0.52x + 0.28y = 0.64(130) (the value of the mixture is $0.64 per pound)

Solving this system of equations, we get x = 50 and y = 80, which means that 50 pounds of $0.52-per-pound beans and 80 pounds of $0.28-per-pound beans are used in the mixture.

This solution is reasonable because it satisfies both equations and makes sense in the context of the problem. The sum of the weights of the two types of beans is 130 pounds, which is the total weight of the mixture, and the value of the mixture is $0.64 per pound, which is the desired value. The amount of the cheaper beans is higher than the amount of the more expensive beans, which is also reasonable since the cheaper beans contribute more to the total weight of the mixture.