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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.

Respuesta :

nobillionaireNobley
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.
anniego4

Answer:

x: number of pounds of beans that sell for $0.72 used

y: number of pounds of beans that sell for $0.52 used

x + y = 110

x = 110 - y

0.72x + 0.52y = 81.4

0.72(110 - y) + 0.52y = 81.4

79.2 - 0.72y + 0.52y = 81.4

79.2 - 0.2y = 81.4

-79.2             -79.2

0.2y = 2.2

/0.2     /0.2

y = 11

x = 110 - y

x = 110 - 11

x = 99

This solution is reasonable because if you combine 99 pounds of beans that sell for $0.72 with 11 pounds of beans that sell for $0.52, then it will equal 110 pounds. It will also be able to be sold at $0.74 a pound.


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