Question

Please help me understand how to work problems like these!

A company sells a container of mixed nuts that is 50% peanuts and another container that is 80% peanuts.

How many cups of each mixture would be needed to make 105 cups that is 60% peanuts?

70 cups of the 50% peanuts and 35 cups of the 80% peanuts
35 cups of the 50% peanuts and 70 cups of the 80% peanuts
55 cups of the 50% peanuts and 50 cups of the 80% peanuts
50 cups of the 50% peanuts and 55 cups of the 80% peanuts

Answer 1

In order to solve for unknowns, you need to have an equal number of equations for all of the unknowns. In this case, you have two unknowns, how many cups of 50% peanuts and how many cups of 80% peanuts.

The goal is to come up with two equations to solve for x and y when
x = cups of 50% peanuts which equal half peanuts
Y = cups of 80% peanuts

This is the hardest of the equations to decipher
0.5x + 0.8y = 0.6(x + y) half peanuts plus eight tenths peanuts equal six tenths of both

Can you figure out the second equation?
If so, I found it easiest to solve the first equation for x and then substitute for x into the second equation and solve for y