# Homework help needed

• Sep 14th 2008, 07:25 PM
Sk9934
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.
• Sep 14th 2008, 08:31 PM
Soroban
Hello, Sk9934!

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

Quote:

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 $\displaystyle x$ = number of tons from Pile A.
Then $\displaystyle 32.5-x$ = number of tons from Pile B.

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

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

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

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

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

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

Got it?