Question

High grade steel consists of 85% iron and 15% magnese. Low grade steel consists of 67% iron and 33% mag ese. NASA orders 500 tons of steel and specifies that it must be in the proportion 80% iron and 20% steel. How many tons of high grade and low grade steel must you melt together to create steel that matches NASA’s requirements?

Answer 1

`361(1)/(9)` tons of high steel and
`138(8)/(9)` tons of low steel

Explanation:

Let x be the number of tons of high grade steel and y be the number of tons ow low grade steel needed.

In x tons of high grade steel there are

`0.85x` tons of iron

`0.15x` tons of magnese

In y tons of low grade steel there are

`0.67y` tons of iron

`0.33y` tons of magnese

NASA orders 500 tons of steel, so

`x+y=500`

and specifies that it must be in the proportion 80% iron and 20% magnese, so

`0.85x+0.67y=500\cdot 0.8\\ \\0.85x+0.67y=400`

From the first equation,

`x=500-y`

Substitute it into the second equation:

`0.85(500-y)+0.67y=400\\ \\425-0.85y+0.67y=400\\ \\-0.18y=-25\\ \\y=(2,500)/(18)=138(8)/(9)\ tons\\ \\x=361(1)/(9)\ tons`