Question

A jeweler wants to combine a 60% gold alloy with a 20% gold alloy to make 1000 grams of 50% gold alloy. How many grams of 60% alloy should be used?

Answer 1

Answer:

750 grams of 60% alloy

Step-by-step explanation:

Define x = amount of 60% alloy and y = amount of 20% alloy

Equating the amounts of gold:

0.6x+0.2y = 1000(0.5)

Since there must be 1000 grams total:

x+y = 1000

Writing the 2 resulting equations together:

0.6x + 0.2y = 500

x + y = 1000

Multiply the first equation by 5:

3x + y = 2500

x + y = 1000

Subtracting the 2nd equation from the 1st:

2x = 1500

x = 750

Answer: 750 grams of 60% alloy