Acoffee 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.

Let x be the number of pounds of beans that sells for $0.72 used and y be the number of pounds of beans that sells for $0.52 used. Then:

x + y = 110 . . . (1)

0.72x + 0.52y = 81.4 . . . (2)

From (1), x = 110 - y . . . (3)

Putting (3) into (2) gives

0.72(110 - y) + 0.52y = 81.4

79.2 - 0.72y + 0.52y = 81.4

79.2 - 0.2y = 81.4

0.2y = 79.2 - 81.4 = -2.2

y = -2.2/0.2 = -11

x = 110 - (-11) = 110 + 11 = 121

The solution is not reasonable because, there cannot be negative value for the number of pounds of beans used.

And 121 pounds of beans cannot produce 110 pounds.

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