SOLUTION: Please help solve: a karat equals 1/24 part of gold in an alloy. (for example 9 karat gold in 9/24 gold) How many grams of a 9 karat gold must be mixed with 18 karat gold to get 20

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Question 261860: Please help solve: a karat equals 1/24 part of gold in an alloy. (for example 9 karat gold in 9/24 gold) How many grams of a 9 karat gold must be mixed with 18 karat gold to get 200 g of 14 karat gold?
Found 2 solutions by richwmiller, solver91311:
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
9/24*x+18/24(200-x)=200*14/24
x=88.89 g of 9 karat gold

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let represent the amount of 9 karat gold. Then represents the amount of pure gold in the unknown amount of 9k gold. Since the total amount must be 200 grams, then the amount of 18k gold must be , and the amount of pure gold in this amount is . The amount of pure gold in the 200 grams of 14k gold must be . The sum of the two amounts of pure gold in the two quantities to be mixed must equal the amount of pure gold in the mixture, so:

Solve for to answer the question. Hint: First multiply both sides of the equation by 24.

John