Question 383884: Rosa bought 1 pound of cashews and 2 pounds of peanuts for $10. At the same store, Sabrina bought 2 pounds of cashews and 1 pound of peanuts for $11. Find the cost per pound for cashews and peanuts.
Answer by jokaehler(26)   (Show Source):
You can put this solution on YOUR website! What you want to do is set the cashews and peanuts as unknown variables. What I will set them as are "x" for cashews and "y" for peanuts.
Let's start with the first sentence.
"Rosa bought 1 pound of cashews and 2 pounds of peanuts for $10."
x + 2y = 10
Let's go to the second sentence.
"Sabrina bought 2 pounds of cashews and 1 pound of peanuts for $11."
2x + y = 11
There are many ways to solve this problem (matrices, substitution, etc.), and I'm going to use substitution. Let's use the second equation to set what "y" is equal to. Subtract 2x to isolate "y"
y = 11 - 2x
Now what we'll do is plug in what we have for "y" into the first equation.
x + 2(11 - 2x) = 10
x + 22 - 4x = 10 (Use the distributive property.)
-3x = -12
x = 4.00
Plug this into the original equations to find "y"
2(4) + y = 11
8 + y = 11
y = 3
4 + 2y = 10
2y = 6
y = 3
So, the solutions are: x = 4. y = 3.
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