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.

Let x be the number of pounds of the $1.35 beans. The cost of those beans is $1.35 * x or 1.35x. 
Let y be the number of pounds of the $1.05 beans. The cost of those beans is $1.05 * y or 1.05y. 
We know that 120 pounds of the mix sell for $1.15/pound, for a total of 120 * 1.15 = $138. 

x + y = 120 
1.35(x) + (1.05)y = 138 

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. 

1.35(x) + 1.05(y) = 138 
1.35(-y + 120) + 1.05y = 138 
-1.35y + 162 + 1.05y = 138 
-0.3y + 162 = 138 
-0.3y = -24 
y = 80 

And since x + y = 120, that means x = 40. 

Check: 
40 pounds of x at $1.35 costs 40 * 1.35, or $54. 
80 pounds of y at $1.05 costs 80 * 1.05, or $84. 
Do those add up to our target total, according to the question, of 120 * 1.15 = $138? 

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)