A chemist has two alloys, one of which is 10% gold and 10% lead and the other which is 40% gold and 30% lead. How many grams of each of the two alloys should be used to make an alloy that contains 67 g of gold and 61 g of lead?

let ist alloy used = x gm

second alloy = y gm

gold = 0.1x + 0.4y

lead = 0.1x + 0.3y

=> x + 4y = 670

=> x + 3y = 610

eqn 1 - eqn 2:

=> y = 60 gm

=> x = 430 gm