Question 1095577
<br>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.<br>
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.<br>
Now that statement is rather awkward, so let me show you the details.<br>
The difference between 24k and 16k is 8k; the difference between 16k and 14k is 2k.<br>
The ratio of those differences is 8:2, or 4:1.<br>
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.<br>
A ratio of 4:1 means 4/5 of the mixture must be one ingredient and 1/5 the other ingredient.<br>
So 4/5 of the 20g, or 16g, is the 14k gold; and 1/5 of the 20g, or 4g, is the pure gold.