document.write( "Question 230461: Sonia has a bag of coins with only nickels and quarters. She has 105 coins that add up to $17.25. How many nickels and quarters does she have? \n" ); document.write( "

Algebra.Com's Answer #170737 by algebrapro18(249) $\"\"$ $\"About$

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Let n be the number of nickles and q be the number of quarters. Then from the problem above we get the system of equations:
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\n" ); document.write( "\n" ); document.write( "n+q = 105
\n" ); document.write( "0.05n+0.25q = 17.25
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\n" ); document.write( "\n" ); document.write( "Just because I hate working with decimals I'm going to multiply the second equation by 100 to get rid of the decimals.
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\n" ); document.write( "\n" ); document.write( "5n + 25q = 1725
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\n" ); document.write( "\n" ); document.write( "Now we can solve the system by using the substitution method. First solve the first equation for n.
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\n" ); document.write( "\n" ); document.write( "n = 105-q.
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\n" ); document.write( "\n" ); document.write( "Now substitute that equation into the second equation and solve for q. I will leave you to do the algebra but you should get that q = 60. Now substitute that back into the equation we found for n and you should find that n = 45.
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\n" ); document.write( "\n" ); document.write( "So Sonia has 60 quarters and 45 nickles. \n" ); document.write( "

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