Precalculus Enhanced with Graphing Utilities
Precalculus Enhanced with Graphing Utilities
6th Edition
ISBN: 9780321795465
Author: Michael Sullivan, Michael III Sullivan
Publisher: PEARSON
Question
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Chapter A.8, Problem 43AYU
To determine

To find: How much 12-karat gold should be mixed with pure gold to obtain 60 grams of 16-karat gold?

Expert Solution & Answer
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Answer to Problem 43AYU

Mix 20 g of pure gold with 40 g .

Explanation of Solution

Given:

The purity of gold is measured 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.

Calculation:

Gold = 60 . ( 16 24 ) = 40 g

Now set up an equation to solve for pure gold + 12k gold.

We know we have 60 grams total weight and 40 g of gold.

Let X be the amount of pure gold in the mixture, then the amount of 12 k gold is 60  x .

Gold content = ( pure Gold . X ) + 12k Gold . ( 60  x )

40 = ( 24 24 ) . X + ( 12 24 ) . ( 60  X )

40 . 24 = 24X + 720  12X

960  720 = 12X

X = 20

So we need to mix 20 g of pure gold with 40 g of 12 k gold to get 60 g of 1.

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