Question

A chemist has two alloy, which is 20% gold and 25% lead and the other which is 30% gold and 40% lead. How many grams of each of the two alloys should be used to make an alloys that contains 116g of gold and 147g of lead

Answer 1

Let x = amount of grams of first alloy

y = amount of grams of second alloy

amount of gold in first alloy = 0.20x

amount of lead in first alloy = 0.25x

amount of gold in second alloy = 0.30x

amount of lead in second alloy = 0.40x

total gold needed in final alloy = 116g

so, 0.20x + 0.30y = 116

total lead needed in final alloy = 147g

so, 0.25x + 0.40y = 147

so, we have two equations-

0.20x + 0.30y = 116

0.25x + 0.40y = 147

solving these,

x = 460g

y = 80g

so, 460g of first alloy, 80g of second alloy.