document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #378533 by math-vortex(648) $\"\"$ $\"About$

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Hi, there--
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\n" ); document.write( "The part-to-part ratio 3:5 represents the amount of copper compared to the amount of gold.
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\n" ); document.write( "However, 85% is part-to-whole; it represents the amount of gold compared to the entire mixture.
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\n" ); document.write( "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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\n" ); document.write( "We see that we need to add more gold to the mixture because 62.5% is less than 85%.
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\n" ); document.write( "Let x be the number of parts of gold we need to add.
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\n" ); document.write( "After this addition, the amount of gold will be 5+x parts.
\n" ); document.write( "After this addition, the total mixture will be 8+x parts.
\n" ); document.write( "After this addition, the percentage of gold will be 85%, or 0.85.
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\n" ); document.write( "The equation is
\n" ); document.write( " $\"%285%2Bx%29%2F%288%2Bx%29=0.85\"$
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\n" ); document.write( "Simplify and solve for x. Multiply both sides of the equation by (8+x) to clear the denominator.
\n" ); document.write( " $\"5%2Bx%29=0.85%288%2Bx%29\"$
\n" ); document.write( " $\"5%2Bx=6.8%2B.85x\"$
\n" ); document.write( " $\"x-0.85x=6.8-5\"$
\n" ); document.write( " $\"0.15x=1.8\"$
\n" ); document.write( " $\"x=1.8%2F0.15\"$
\n" ); document.write( " $\"x=12\"$
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\n" ); document.write( "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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\n" ); document.write( "CHECK your work.
\n" ); document.write( "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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\n" ); document.write( "That's it. Feel free to email me via gmail, if you have questions about this solution.
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\n" ); document.write( "Ms.Figgy
\n" ); document.write( "math.in.the.vortex@gmail.com \n" ); document.write( "

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