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A metal alloy that is made up of 15% aluminum is combined with a metal alloy that is 35% aluminum. If the result is 400 Kilograms of 27.5% of aluminum alloy, then how much of each alloy was used?

Respuesta :

1. Assume that the types of metal allow we use are type A and type B

2. Assume we are using x kg of A and y kg of B

3. Then x+y=400, so y=400-x

also the weight of the aluminium in x kg of A and y kg of B are respectively:

[tex] \frac{15}{100}*x=0.15x [/tex] and

[tex]\frac{35}{100}*y=0.35y [/tex]

so the total sum of the aluminium is [tex]0.15x+0.35y=0.15x+0.35(400-x)=0.15x+140-0.35[/tex] [tex]=140-0.2x[/tex]

4. 27.5% of 400 is [tex] \frac{27.5}{100}*400=27.5*4= 110[/tex] kg 

5. [tex]140-0.2x=110[/tex]

     [tex]140-110=0.2x[/tex]

[tex]0.2x=30[/tex]

x=150 (kg), 

y=400-x=400-150=250(kg)

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