SOLUTION: One alloy is one part copper to three parts tin. A second alloy is one part copper to four parts tin. How much of the second alloy should be combined with 24 pounds of the first al

Question 160286: One alloy is one part copper to three parts tin. A second alloy is one part copper to four parts tin. How much of the second alloy should be combined with 24 pounds of the first alloy to obtain a new alloy that is two parts copper to seven parts tin?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
One alloy is one part copper to three parts tin. A second alloy is one part copper to four parts tin. How much of the second alloy should be combined with 24 pounds of the first alloy to obtain a new alloy that is two parts copper to seven parts tin?
.
Let x = pounds of second alloy to be added
.
From: "One alloy is one part copper to three parts tin."
we know that:
total of four parts
.25 is copper
.75 is tin
.
From: "A second alloy is one part copper to four parts tin."
total of four parts
.20 is copper
.80 is tin
.
We want:
2/9 copper
7/9 tin
.
Just consider the copper (we could have considered tin or copper -- didn't matter):
.25(24) + .20x = (2/9)(24+x)
.25(24) + .20x = (2/9)(24+x)
6 + .20x = (2/9)(24+x)
54 + 1.8x = (2)(24+x)
54 + 1.8x = 48+2x
6 = .2x
30 pounds = x

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