SOLUTION: A food store makes a 9-lb mixture of peanuts. cashews, and raisens. Peanuts cost $1.50 per pound, cashews cost $2.00 per pound, and raisens cost $1.00 per pound. The mixture calls

Question 173475: A food store makes a 9-lb mixture of peanuts. cashews, and raisens. Peanuts cost $1.50 per pound, cashews cost $2.00 per pound, and raisens cost $1.00 per pound. The mixture calls for twice as much peanuts than cashews. The total cost of the mixture is $13.00. How much of each ingredient did the store use?
How do you det this up into equations?
Found 2 solutions by Mathtut, josmiceli:
Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!
let the number of peanuts, cashews, and raisens be p,c,and r respectively
:
p+c+r=9........eq 1----->r=9-p-c
1.5p+2c+1r=13..eq 2
p=2c...........eq 3
:
lets plug p's value in eq 3 into eq 1 and 2 and re write them
:
2c+c+r=9.........eq (4)
1.5(2c)+2c+r=13..eq (5)
:
3c+r=9.... eq (4)
5c+r=13... eq (5)
:
now lets subtract eq 5 from eq 4
:
-2c=-4
:
pounds of cashews
:
pounds of peanuts
:
pounds of raisens

Answer by josmiceli(6784) (Show Source):
You can put this solution on YOUR website!
These problems are always easier if you put letters in place
of the things you're looking for:
Let = the pounds of peanuts needed
Let = the pounds of cashews needed
Let = the pounds of raisins needed
The 1st sentence says it's a 9-pound mixture, so
(1)
Peanuts cost $1.50 per pound, so the cost of the peanuts will be

Cashews cost $2.00 per pound, so the cost of the cashews will be

Raisins cost $1.00 per pound, so the cost of the raisins will be

The total cost of the mixture is $13.00, so
(2)
The mixture calls for twice as much peanuts than cashews, so
(3)
Now I have 3 equations and 3 unknowns, so it should be solvable
Subtract (1) from (2)

Substitute (3) for

And, going back to (3),

Use (1) to find

The amounts of the ingredients are 2 pounds of cashews,
4 pounds of peanuts, and 3 pounds of raisins
Check answer:
(2)

OK