Question 598292: A chemist made a mixture of 3 parts of copper and 5 parts of gold. He wants to change the mixture so that is 85% gold.
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! Hi, there--
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The part-to-part ratio 3:5 represents the amount of copper compared to the amount of gold.
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However, 85% is part-to-whole; it represents the amount of gold compared to the entire mixture.
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First, convert the part-to-part ratio to a percentage. There are 3+5=8 parts of mixture for every 5 parts gold; 5/8=0.625. We can write 0.625 as the percentage, 62.5%.
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We see that we need to add more gold to the mixture because 62.5% is less than 85%.
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Let x be the number of parts of gold we need to add.
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After this addition, the amount of gold will be 5+x parts.
After this addition, the total mixture will be 8+x parts.
After this addition, the percentage of gold will be 85%, or 0.85.
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The equation is
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Simplify and solve for x. Multiply both sides of the equation by (8+x) to clear the denominator.
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The equation x=12 means that we must add 12 parts of gold to the mixture to make it 85% gold.
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CHECK your work.
If we add 12 parts of gold, we have 5+12=17 parts of gold compared to 8+12=20 parts total. We divide: 17/20 = 0.85 or 85%.
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That's it. Feel free to email me via gmail, if you have questions about this solution.
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Ms.Figgy
math.in.the.vortex@gmail.com
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