Borris is working with copper alloys

Question

Boris is working with an alloy that is​ 5% copper. He needs to increase its copper content to​ 8% by adding in an amount of alloy that is​ 10% copper. If he needs 2 grams of the​ 8% copper​ alloy, how much of the​ 10% alloy should he​ add?

Answer 1

First, rephrase the question as two sets of mathematical equations:

x: mass of 5% alloy y: mass of 10% alloy

x + y = 2 (sum of alloy mass equals 2 g)

1/2*(5x + 10y) = 8 (average percentage of copper equals 8%)

Next, solve for x in terms of y

x = 2 - y

Finally, plug in solution into the second equation to find actual value of y

1/2*(5(2-y) + 10y) = 8

1/2*(10 - 5y + 10y) = 8

1/2*(10 + 5y) = 8

5y = 16 - 10

y = 6/5

So, the answer should be that 1.2 g of 10% alloy is needed to obtain 2 g of 8 % alloy.

Answer 2

5X + 10(2-X) = 8(2) = 16

5X-10X = 16-20 = -4

5X =4

X = 4/5 = 0.8 g of 5% alloy

2-X = 1.2 g of 10% alloy

mixed to get 2 g of 8% alloy

10 is 2 from 8

5 is 3 from 8

10 is closer, you want more of 10 than of 5 to get to 8

10 is 1.5 times closer 3/2=1.5

1.2 = 3/2 x .08

you want