Peanuts sell for $3.00 per pound. Cashews sell for $6.00 per pound. How many pounds of cashews should be mixed with 12 pounds of peanuts to obtain a mixture that sells for $4.20 per pound?
C*6+12*3=(C+12)4.20
amount of cashews ---- x pounds
amount of peanuts ---- 12-x pounds
6x + 3(12-x) = 4.2(12)
6x + 36 - 3x = 50.4
3x = 14.4
x = 4.8
need 4.8 pounds of cashews and 7.2 pounds of peanuts
Proof:
6(4.8) + 3(7.2)
= 50.4
cost per pound = 50.4/12 = 4.2
Ignore my solution
Didn't read the question careful enough
go with bobpursley's solution
To find the answer, we'll use the concept of weighted averages. The price per pound of the mixture will be the weighted average of the prices per pound of peanuts and cashews.
Let's assume we need to mix x pounds of cashews with the 12 pounds of peanuts.
The weighted average equation is:
(price per pound of peanuts * pounds of peanuts) + (price per pound of cashews * pounds of cashews) = price per pound of mixture * total pounds of mixture
Substituting the given values:
($3.00/pound * 12 pounds) + ($6.00/pound * x pounds) = $4.20/pound * (12 pounds + x pounds)
Now we can solve the equation to find the value of x, which represents the pounds of cashews needed.
Multiply the prices per pound of peanuts and cashews by their respective amounts:
36 + 6x = 50.4 + 4.2x
Rearrange the equation by moving the x terms to one side:
6x - 4.2x = 50.4 - 36
1.8x = 14.4
Divide both sides by 1.8 to isolate x:
x = 14.4/1.8
x = 8
So, you need to mix 8 pounds of cashews with the 12 pounds of peanuts to obtain a mixture that sells for $4.20 per pound.