Question

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?

Answer 1

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:


`(15)/(100)*x=0.15x` and


`(35)/(100)*y=0.35y`

so the total sum of the aluminium is
`0.15x+0.35y=0.15x+0.35(400-x)=0.15x+140-0.35`
`=140-0.2x`

4. 27.5% of 400 is
`(27.5)/(100)*400=27.5*4= 110` kg

5.
`140-0.2x=110`


`140-110=0.2x`


`0.2x=30`

x=150 (kg),

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