SOLUTION: A karat equals 1/24 part of gold in any alloy ( for example, 9-karat gold is 9/24 gold). How many grams of 9-karat gold must be mixed with 18-karat gold to get 200g of 14-karat gol

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Question 159586: A karat equals 1/24 part of gold in any alloy ( for example, 9-karat gold is 9/24 gold). How many grams of 9-karat gold must be mixed with 18-karat gold to get 200g of 14-karat gold?
Answer by ankor@dixie-net.com(22740) (Show Source):
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A karat equals 1/24 part of gold in any alloy ( for example, 9-karat gold is 9/24 gold). How many grams of 9-karat gold must be mixed with 18-karat gold to get 200g of 14-karat gold?
:
Let x = amt of 18 karat gold
then
(200-x) = amt 9 karat gold
;
x + (200-x) = (200)
:
We can get rid of all those denominators by multiplying by 24:
18x + 9(200-x) = 14(200)
:
18x + 1800 - 9x = 2800
;
18x - 9x = 2800 - 1800
:
9x = 1000
x =
x = 111.11 gr of 18 karat gold
and
200 - 111.11 = 88.89 gr of 9 karat gold