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Like us? Trail mix, mixture word problem

Q: The manager of a bulk foods establishment sells a trail mix for \$10 per pound and premium cashews for \$15 per pound. The manager wishes to make a 100-pound trail mix-cashew mixture that will sell for \$14 per pound. How many pounds of each should be used?

A: Let x = pounds of trail mix
Let y = pounds of cashews

The two amounts have to add up to 100 pounds, so that gives us the first equation:

x+y = 100

Next, we know that the 100-pound mixture needs to cost \$14 per pound. We can use the per pound information for the trail mix and cashews to make equation 2:

10x + 15y = 14*100

Now use whatever method you like to solve the equations. I will choose to use substitution method:

y = 100-x

10x + 15(100-x) = 1400
10x +1500 -15x = 1400
100 = 5x
x = 20

Use equation 1 to find y:

x+y = 100
y = 80

So there should be 20 pounds of trail mix and 80 pounds of cashews.