Acoffee mixture has beans that sell for $0.20 a pound and beans that sell for $0.68. if 120 pounds of beans create a mixture worth $0.54 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 amount of beans in mixture for $0.20 a pound  and y be the amount of beans in mixture for $0.68 a pound.  If 120 pounds of beans create a mixture, then

x+y=120.

x pounds beans for $0.20 a pound  cost $0.20x and y pounds beans for $0.68 a pound cost $0.68y. If mixture worth $0.54 a pound, then it costs $0.54·120=$64.8 for 120 pounds. Then

0.20x+0.68y=64.8

You get the system of equations:

Solve it.

1. Multiply second equation by 100:

2. Express x from first equation and substitute it in second:

3. The equation 20(120-y)+68y=6480 contains only y and is easy to solve:

2400-20y+68y=6480,

48y=6480-2400,

48y=4080,

y=85.

4. Then x=120-y=120-85=35.

you should take 35 pounds of beans for $0.20 a pound  and 85 pounds of beans for $0.68 a pound.

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