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 wo

Question

2 years ago

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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 wo

rth $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.

Mathematics

2 answers:

Deffense [45] · Answer 1 · 2023-12-07T22:02:34+03:00

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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alekssr [168] · Answer 2 · 2023-12-07T19:41:52+03:00

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.