Web Analytics
Briscalwanp
Answered

A coffee 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.

Verified Answer :

Let x be the number of pounds of the $.20 beans.
The cost of those beans is $.20 x, or .20x. 

Let y be the number of pounds of the $.68 beans. The
cost of those beans is $ .68 y, or .68y. 

We know that 120 pounds of the mix sells for $ 0.54/pound,
for a total of 120 * 0.54 = $ 64.8


x + y = 120 

1.35(x) + (1.05)y = 64.8


We can rewrite the first as 

x = -y + 120 


Now we can substitute (-y + 120) in for (x) in the
second equation, because we just proved they're equal. 


.20(x) + .68(y) = 64.8 

.20(-y + 120) + .68y = 64.8

-.20y + 24 + .68y = 164.8

-0.3y + 24 = 64.8 

-0.38y = -24 

y = 63.16

Related Questions