SOLUTION: Suppose you combine ingots of 25% copper alloy and 50% copper alloy to create 40 kg of 45% copper alloy. How many kilograms of each do you need? Select one: a. 80 kg 25%

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Question 574962: Suppose you combine ingots of 25% copper alloy and 50% copper alloy to create 40 kg of 45% copper alloy. How many kilograms of each do you need?

Select one:

a. 80 kg 25% alloy; 40 kg 25% alloy
b. 32 kg 50% alloy; 8 kg 25% alloy
c. 0 kg 25% alloy; 40 kg 50% alloy
d. 25 kg 50% alloy; 15 kg 25% alloy
I need help can't get the answer!
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
x = amount of the first solution.
y = amount of the second solution.
x + y = 40 kg of the combined solution.
.25x is the amount of copper alloy in the first solution.
.50x is the amount of copper alloy in the second solution.
.45 * 40 is the amount of copper alloy in the combined solution.
you have 2 equations.
x + y = 40
.25x + .50y = .45*40
the first equation tells you the total amount of the new solution.
the second equation tells you the amount of copper alloy in the new solution.
solve these 2 equations simultaneously for your answer.
from the first equation, solve for x to get:
x = 40 - y
substitute this value for x in the second equation to get:
.25(40-y) + .5y = .45*40
simplify to get:
.25*40 - .25y + .5y = .45*40
combine like terms to get:
.25*40 + .25y = .45*40
subtract .25*40 from both sides of the equation to get:
.25y = .45*40 - .25*40
factor the right side of the equation to get:
.25y = 40*(.45-.25)
simplify to get:
.25y = 40*(.20)
simplify further to get:
.25y = 8
divide both sides of this equation by .25 to get:
y = 32
since x + y = 40, this means that:
x = 8
you need 8 kilograms of 25% copper alloy and 32 kilograms of 50% copper alloy to get 40 kilograms of 45% copper alloy.
8 + 32 = 40
.25*8 + .5*32 = 2 + 16 = 18
18 / 40 = 45% copper alloy in the new solution.