SOLUTION: I have an algebra question for you, to which I require assistance, as I am not quite certain what it is they want me to do. It is a written question. An alloy contains 60% by we

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Question 94750: I have an algebra question for you, to which I require assistance, as I am not quite certain what it is they want me to do. It is a written question.
An alloy contains 60% by weight of copper, the remainder being zinc. How much copper must be mixed with 50kg of this alloy to give an alloy containing 75% copper?
I have done some nuber crunching and all I got was
60% of 50kg = 30kg
and
75% of 50kg = 37.5kg
and or
60x+40y=50
75x+25y=50 /5
60x+40y=50 /4
15x+5y=10
15x+10y=12.5
15x+5y=10
anyhow
X = .5kg
and
Y = .5kg
but it just does not look right, would you please be able to show me the correct way to sort this out. It would be greatly appreciated. Thank you.
Found 2 solutions by Earlsdon, edjones:
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
First, let's concentrate on the amount of copper (Cu) in the starting alloy and the resulting alloy.
The amount of copper in the starting alloy is: 60% of 50 kg or (0.6)(50). To this we want to add x kg of Cu to make (50+x) kg of an alloy, 75% of which is Cu. So we set up the equation:
(0.6)(50) + x = (0.75)(50+x) Simplify and solve for x.
30+x = 37.5+0.75x Subtract 0.75x from both sides.
30+0.25x = 37.5 Subtract 30 from both sides.
0.25x = 7.5 Finally, divide both sides by 0.25
x = 30
You would need to add 30kg of Cu to the 50kg of the starting alloy to obtain 80kg (50kg + 30kg) of the resulting alloy containing 75% Cu.
Check:
50(0.6)+30 = (50+30)(0.75)
30+30 = (80)(0.75)
60 = 60

Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
Table making is more important than number crunching in mixture problems.
=====gross wt.copper wt.
60%====50======0.6*50
100%====x=======1*x
75%====x+50==.75(x+50)
now we can make an equation out of the 3rd column.
.6*50+x=.75(x+50)
30+x=.75x+37.5
subtract .75x and 30 from both sides. .25x=7.5
divide both sides by .25
x=30kg. of copper that must be added
EdJones