SOLUTION: cashews sell for $5 per pound and peanuts sell for $2 per pound. How many pounds of each would you use to make 21 pounds of a mixture that sells for $3.00 per pound?

Question 148915: cashews sell for $5 per pound and peanuts sell for $2 per pound. How many pounds of each would you use to make 21 pounds of a mixture that sells for $3.00 per pound?
Found 2 solutions by nabla, mangopeeler07:
Answer by nabla(475) (Show Source): You can put this solution on YOUR website!
C(s)=5s
P(t)=2t
where s is the amount of pounds of cashews, and t is the amount of pounds of peanuts.
We want
(C(s)+P(t))/(s+t)=3
and
s+t=21
thus,
C(s)+P(t)=63
5s+2t=63.
s+t=21--->s=21-t
5(21-t)+2t=63
-3t=-42
t=14
If t=14,
5s+28=63
5s=35
s=7
So we want a mixture of 7 lb of cashews and 14 lb of peanuts in order to make 21 lb of mixture that will sell for $3./lb.

Check:
7*5=35
2*14=28
35+28=63
$63/21 lb=$3/lb

Answer by mangopeeler07(462) (Show Source): You can put this solution on YOUR website!
x=# pounds of cashews
y=# pounds of peanuts

5x+2y=63--------------Because the cost of it all is 21 times 3 (21 pounds of a mixture that sells for $3.00 per pound)

x+y=21

So you have two equations
5x+2y=63
x+y=21

Solve for x in the second equation
x=21-y

Plug that into the first equation
5(21-y)+2y=63

Distribute
105-5y+2y=63

Combine like terms
105-3y=63

Subtract 105 from both sides
-3y=-42

Divide by -3
y=14

That is the pounds of peanuts
plug that into the second equation
x+14=21

Subtract 14 from both sides
x=7

That is the pounds of cashews
So,

14 lbs. peanuts
7 lbs. cashews
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