Question

Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of sue and jane's trails mix contains 50% nuts, what percent of the combined mixture is dried fruit?

Answer 1

Let's say that the combined mixture weighs 100 pounds.

If the combined mix is 50% nuts, then there are 50 pounds of nuts in the combined mixture.

Let's let x = the # of pounds of Sue's trail mix

This means that 100-x = the # of pounds of Jane's trail mix

My word equation: (# of pounds of nuts in Sue's portion) + (# of pounds of nuts in Jane's portion) = 50

In other words: (30% of x) + (60% of 100-x) = 50

Rewrite as: 0.3x + 0.6(100-x) = 50

Expand: 0.3x + 60 - 0.6x = 50

Simplify: -0.3x = -10

Solve: x = 10/0.3 = 100/3 = 33.3333..