How do I solve this?

Question

A metalworker has a metal alloy that is 25​% copper and another alloy that is 60​% copper. How many kilograms of each alloy should the metalworker combine to create 100kg of a 46​% copper​ alloy?

Answer 1

First notice 46 is closer to 60 than to 25, so you want more of the 60% than of the 25%

and the sum of the quantities will add to 100 kg.

Let T=the 25% copper amount needed and S= the 60% amount needed

T+S=100 the amounts have to sum to 100 kg, so T=100-S S will bigger than 50, T less than 50 kg

.25T + .60S = .46(100)

.25(100-S) + .6S = 40

25-S/4 + .6S =46

(.6-.25)S=21

.35S=21

35S=2100

5S=300

S=60 kg

T=100-S=100-60=40

check the answer. S+T=100 kg

.25T+.6S=.46(100)=40

(1/4)(40) + .6(60)=

10+36=46 kg