1. ## Homework help needed

Steel is an alloy of iron and nickel. A steel recycling company has two piles of scrap steel. Pile A contains steel with 5.25% nickle content. Pile B contains steel with 2.84% nickel. The company has an order for 32.5 tonnes of steel containing 4.15% nickle. How mach scrap steel should be taken from each pile for reprocessing?

Thanks.

2. Hello, Sk9934!

What ugly numbers!
Couldn't they have chosen "better" numbers?

Steel is an alloy of iron and nickel.
A steel recycling company has two piles of scrap steel.
Pile A contains steel with 5.25% nickel content.
Pile B contains steel with 2.84% nickel.
The company has an order for 32.5 tons of steel containing 4.15% nickel.
How mach scrap steel should be taken from each pile for reprocessing?
Let $x$ = number of tons from Pile A.
Then $32.5-x$ = number of tons from Pile B.

The $x$ tons from Pile A is 5.25% nickel.
. . It contains: . $0.0525x$ tons of nickel.

The $32.5-x$ tons from Pile B is 2.84% nickel.
. . It contains: . $0.0284(32.5 - x)$ tons of nickel.

Hence, the total amount of nickel is: . $0.025x + 0.0284(32.5 - x)$ tons. .[1]

But we are told that the mixture will be 32.5 tons which is 4.15% nickel.
. . This contains: . $0.0415 \times 32.5 \:=\:1.34875$ tons of nickel. .[2]

We just described the final amount of nickel in two ways.

There is our equation! . . . ${\color{blue}[1] = [2]} \hdots\;\;0.0525x + 0.0284(32.5-x) \;=\;1.34875$

Got it?