Question

How much of an alloy with 30% copper must be added to 25 pounds of a second alloy that is 20% copper to create a 27% alloy? 33.85 lb 58.33 lb 391.67 lb

Answer 1

The answer should be B or the second option. :)

Answer 2

58.33 lbs.

Explanation:

There are already 25 lbs of alloy of copper

Of this 25 lbs, 20% is pure i.e. copper content = 25(0.5) = 5lbs.

Now available is

Copper Other metals

5 lbs 20 lbs

Let x lb of 30% copper is added.

Then new alloy will have 5+0.3x lb copper in total of 25+x lbs

Percentage pure =
`(5+0.3x)/(25+x) =27%`

Simplify to get

`(5+0.3x)/(25+x) =(27)/(100) \\\\Cross multiply:\\27(25+x) =100(5+0.3x)\\500+30x =675 +27x\\3x = 175\\x = 175/3 = 58.33 lbs`

Hence answer is 58.33 lbs should be added.