Question 653313: How many pounds of cashews worth 5.00 per pound and how many pounds of peanuts worth 2.00 per pound would you mix to get an 18 pound mixture worth 3.00 per pound?
Answer by Shana-D77(132)   (Show Source):
You can put this solution on YOUR website! Ugh, mixture problems, right? These took me a long time to get! The only good thing is that we always do these peoblems the same way:
First, we need to set up two equations.
One equation is "value"
The other equation is "amount"
The amount equation is easy:
Let x = pounds of cashews
Let y = pounds of peanuts
Given 18 = pounds of mixture
So x + y = 18
The value equation is a little tricky.
The value of cashews is 5 per pound. So "5x"
The value of peanuts is 2 per pound. So "2y"
The value of the mix is 3 per pound. The mix is (x + y), so the value is 3(x + y). That's the trickiest part!
We put those pieces together and we get:
5x + 2y = 3(x + y)
5x + 2y = 3x + 3y (distrubuted the 3)
2x + 2y = 3y (subtracted 3x from both sides)
2x = y (subtracted 2y from both sides)
y = 2x (turned around)
Our value equation is y = 2x
Our amount equation was x + y = 18
Now we use substitution:
if y = 2x and:
x + y = 18 then:
x + (2x) = 18
3x = 18 (combined like terms)
x = 6 (divided both sides by 3)
You will need 6 pounds of cashews.
Remember how x + y = 18?
Then you need:
6 + y = 18
y = 12
You need 12 pounds of peanuts and 6 pounds of cashews.
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