Answer:
[tex]361\dfrac{1}{9}[/tex] tons of high steel and [tex]138\dfrac{8}{9}[/tex] tons of low steel
Step-by-step 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
[tex]0.85x[/tex] tons of iron
[tex]0.15x[/tex] tons of magnese
In y tons of low grade steel there are
[tex]0.67y[/tex] tons of iron
[tex]0.33y[/tex] tons of magnese
NASA orders 500 tons of steel, so
[tex]x+y=500[/tex]
and specifies that it must be in the proportion 80% iron and 20% magnese, so
[tex]0.85x+0.67y=500\cdot 0.8\\ \\0.85x+0.67y=400[/tex]
From the first equation,
[tex]x=500-y[/tex]
Substitute it into the second equation:
[tex]0.85(500-y)+0.67y=400\\ \\425-0.85y+0.67y=400\\ \\-0.18y=-25\\ \\y=\dfrac{2,500}{18}=138\dfrac{8}{9}\ tons\\ \\x=361\dfrac{1}{9}\ tons[/tex]
