SOLUTION: The manager of a specialty food store combined almonds that cost $4.50 per pound with walnuts that cost $2.50 per pound. How many pounds of each were used to make a 100-pound mixtu

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Question 162206: The manager of a specialty food store combined almonds that cost $4.50 per pound with walnuts that cost $2.50 per pound. How many pounds of each were used to make a 100-pound mixture that cost $3.23 per pound?
Found 2 solutions by checkley77, jojo14344:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
4.50x+2.50(100-x)=3.23*100
4.50x+250-2.5x=323
2x=323-250
2x=73
x=73/2
x=36.5 pounds of $4.50 almonds are used.
100-36.5=63.5 pounds of $2.50 walnuts are used.
Proof:
4.5*36.5+2.5*63.5=323
164.25+158.75=323
323=323

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

A%2BW=100lbs -------------> EQN 1, Almond and walnuts mixed produced 100lbs
In EQN 1 we get,
A=100lbs-W -------------> EQN 2
Also take note,
4.50A%2B2.50W=100lbs%283.23%2Flb%29 -------------------> EQN 3
Subst. EQN 2 in EQN 3:
4.50%28100-W%29%2B2.50W=323, distribute
450-4.50W-2.50W=323, combine similar terms
450-323=4.50-2.50W
127=2W --------> cross%28127%2963.5%2Fcross%282%29=cross%282%29W%2Fcross%282%29
highlight%28W=63.5lbs%29
For Almonds, go back EQN 2,
A=100-63.50
highlight%28A=36.50lbs%29
In doubt? Go back EQN 3,
4.50%2836.50%29%2B2.50%2863.50%29=100%283.23%29
164.25%2B158.75=323
323=323
Thank you,
Jojo