SOLUTION: A gift store is making a mixture of almonds, pecans, and peanuts, which sells for $3.50 per pound, $3 per pound, and $2 per pound, respectively. The storekeeper wants to make 50 po

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Question 965681: A gift store is making a mixture of almonds, pecans, and peanuts, which sells for $3.50 per pound, $3 per pound, and $2 per pound, respectively. The storekeeper wants to make 50 pounds of mix to sell at $3.20 per pound. The number of pounds of peanuts is to be three times the number of pounds of pecans. Find the number of pounds of each to be used in the mixture?
I actually really like solving systems of equations, but I am having a hard time setting this one up to begin with! I will appreciate any help, and thanks in advance!
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
VARIABLES
x, y, z, for almonds, pecans, peanuts

Prices are given.

Account for the 50 pound mixture:
x%2By%2Bz=50

Account for the COST of the mixture:
3.5x%2B3y%2B2z=50%2A%283.2%29

Express poundage relationship for the peanuts to pecans:
y%2Fz=3

The poundage account starts as it is.
The cost account should be simplified and to have if possible (yes) integer coefficients, so
%283.5x%2B3y%2B2z%29%2A2=50%283.2%29%2A2
7x%2B6y%2B4z=320
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The ratio equation should be made into a formula for one of the variables:
y=3z

You now have this equivalent system of equations:
highlight%28system%28x%2By%2Bz=50%2C7x%2B6y%2B4z=320%2Cy=3z%29%29

You should be able to solve this system with little trouble. You can start by making the very obvious substitution for y. Simplify and you have from that, two equations in two unknowns...