A chemist has two alloys one of which is 10 gold and 20 lead

A chemist has two alloys, one of which is 10% gold and 20% lead and the other which is 20% gold and 30% lead. How many grams of each of the two alloys should be used to make an alloy that contains 61 g of gold and 113 g of lead?

Solution

let amount of first alloy = x gram and second alloy = y gram

then for the gold: 10% of x + 20% of y = 61

x + 2y = 610....(1)

and for lead:

20% of x + 30% of y = 113

2x + 3y = 1130 .....(2)

solve first and second equation:

put x = 610 - 2y in second equation:

2(610 - 2y) + 3y = 1130

1220 - 4y + 3y = 1130

-y = 1130 - 1220 = -90

y = 90

and then x = 610 - 2*90 = 610 - 180 = 430

then first alloy = 430 gram and second alloy = 90 gram