SOLUTION: a 10-lb mixture of peanuts, cashews, and raisins sell for $14. Peanuts cost $1 per pound, cashews cost $2 per pound, and raisins cost $1.50 per pound. The weight of peanuts in the

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Question 830370: a 10-lb mixture of peanuts, cashews, and raisins sell for $14. Peanuts cost $1 per pound, cashews cost $2 per pound, and raisins cost $1.50 per pound. The weight of peanuts in the mixture is twice the weight of cashews in the mixture.
A. write a system of equations that represent the problem
B. find the number of pounds of each ingredient in the mixture.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Pounds of peanuts, cashews, raisins as p,c, r.
Prices: 1 dollars per pound peanuts, 2 dollars per pound cashews, 1.50 dollars per pound raisins.
Price of mixture: $14.
p=2c.

Accounting for price of mixture: 1%2Ap%2B2%2Ac%2B1.5%2Ar=14;
Accounting for pounds: p%2Bc%2Br=10.

Substitute for p in the two accounting equations and simplify:
2c+2c+1.5r=14
4c+1.5r=14
To use all integer coefficients multiply by 2...
highlight_green%288c%2B3r=28%29
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2c+c+r=10
highlight_green%283c%2Br=10%29

Solve the simultaneous equations highlighted with green.
3c%2Br=10 is the same as 9c%2B3r=30;
-
%289c%2B3r%29-%288c%2B3r%29=30-28
highlight%28c=2%29-
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p=2c
p=2*2
highlight%28p=4%29
-
Use either of the accounting equations to find the value for r.
Using 3c+r=10
r=10-3c
r=10-3*2
highlight%28r=4%29