Question

Juan wants to make a trail mix that contains 40% pecans. He has a bag of trail mix that has only 25% pecans at home and another bag that contains only pecans. How much of each should be mixed together to make a 16oz bag of trail mix that contains 40% pecan?

Answer 1

Stuff from his trail mix is 25% pecans. If we use \(x\) to represent the quantity of trail mix, the amount of pecans will be 0.25x.

Stuff from the straight pecan bag is obviously 100% pecans. If we use \(y\) to represent the quantity of straight pecans, the amount of pecans will be 1y.

We know that x+y = 16 if we are producing 16 oz of trail mix containing 40% pecans.

We also know that 16 oz of trail mix with 40% pecans will contain 0.4*16 oz of pecans.
That gives us a second equation: 0.25x + 1y = 0.4*16

Solve the system containing those two equations, and you'll have your answer.