Mike, the barista at Moose Jaw Coffee, has to mix together two kinds of coffee beans - Mocha Madness, which costs $12 a pound, and Sumatra Sweetness, which costs $20 a pound - to produce forty pounds of a coffee that costs $14 a pound. The beans in the mixture sell for the same price as they would separately. How many pounds of Mocha Madness coffee will Mike put into the mixture

mocha madness = 30 pounds

Step-by-step explanation:

Let

x =  Mocha Madness

y = Sumatra Sweetness

two equations can be derived from the question

x + y = 40 equation 1

12x + 20y = 14 x 40 equation 2

Multiply equation 1 by 12

12x + 12y = 480 eqn 3

subtract eqn 2 from 3

8y = 80

y = 10

substitute for y in equation 1

x + 10 = 40

x = 40 - 10

x = 30

8y = 180

y = 10 pounds

x = 30 pounds

47 - 90 = 43

43 - 180 = x

x = 137