Question 1095577: Hello Tutors,
the problem I am having trouble with is the following:
The purity of gold is measure in karats, with pure gold being 24 karats. Other purities of gold are expressed as proportional parts of pure gold. Thus 18 karat gold is 18/24 or 75% pure gold, 12 karat gold is 12/24 or 50% pure gold and so on. How much 14-karat gold should be mixed with pure gold to obtain 20 grams of 16-karat gold?
I have tried a formula and I get the answer 3.2 but when I submit it it said that the correct answer is 16 (which I think is wrong). If you can help me clarify if that is the answer or what would the real answer be, I really appreciate it.
Thank you!
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Here is an alternative to the traditional algebraic solution shown by the other tutor. See if it makes sense to you; if you understand it, you can solve mixture problems like this much faster and with much less work than by the traditional algebraic method.
The ratio in which the two ingredients (14k gold and pure, 24k gold) must be mixed to get 16k gold is exactly the same as the ratio of how far the 16k is from the 14k and 24k.
Now that statement is rather awkward, so let me show you the details.
The difference between 24k and 16k is 8k; the difference between 16k and 14k is 2k.
The ratio of those differences is 8:2, or 4:1.
That means the two ingredients must be mixed in the ratio 4:1; and since 16k is closer to 14k than to 24k, the larger portion must be the 14k gold.
A ratio of 4:1 means 4/5 of the mixture must be one ingredient and 1/5 the other ingredient.
So 4/5 of the 20g, or 16g, is the 14k gold; and 1/5 of the 20g, or 4g, is the pure gold.
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