Question

a chemist has two alloys, one of which is 10% gold and 15% lead and the other of which is 30% gold and 40% lead. how many grams of each of the two alloys should be used to make an alloy that contains 60 grams of gold and 88 grams of lead

Answer 1

Let the weight of the first alloy will be x grams.
Weight of gold will be 0.1x grams, weight of lead will be 0.15x grams.
Let the weight of the second alloy will be y grams.
Weight of gold will be 0.3y grams, weight of lead will be 0.4y grams.
Summarizing:
0.1x+0.3y=60       - gold
0.15x+0.4y=88     - lead

0.1x+0.3y=60     * 10   
0.15x+0.4y=88   * 100

x+3y=600          * 15
15x+40y=8800

15x+45y=9000      
15x+40y=8800

15x+45y=9000            /15
45y-40y=9000-8800

x+3y=600     
5y=200

x+3y=600     
y=40

y=40
x=600-3*40=480

y=40    
x=480

↑The answers.