SOLUTION: Susan wants to mix 10 pounds of Virginia peanuts that cost $3.50 a pound with Spanish peanuts that cost $3.00 a pound to obtain a mixture that costs $3.40 a pound. How many pounds

Question 452750: Susan wants to mix 10 pounds of Virginia peanuts that cost $3.50 a pound with Spanish peanuts that cost $3.00 a pound to obtain a mixture that costs $3.40 a pound. How many pounds of Spanish peanuts should she use?
I have given this problem some thought but I do not know how you would solve.
Thanks

Answer by ilana(307) (Show Source): You can put this solution on YOUR website!
There will be 10 pounds of Virginia peanuts and x pounds of Spanish peanuts. The total cost will be 3.5(10) + 3(x). The total amount of pounds will be 10 + x. You want the cost per pound to be $3.40, so the (total cost)/(total pounds) should be 3.4, so solve the equation:
(35 + 3x)/(10 + x) = 3.4
35 + 3x = 3.4(10 + x)
35 + 3x = 34 + 3.4x
1 = 0.4x
x = 1/(4/10)
x = 10/4
x = 2.5
She should use 2.5 pounds of Spanish peanuts.
Then the total cost will be 35 + 7.5, or $42.50.
The total weight will be 10 + 2.5, or 12.5 pounds.
The total cost per pound will be 42.5/12.5 = $3.40/pound.

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