document.write( "Question 215018: You have 15 coins in your pocket that are either quarters or nickles. the total $2.75. how many of each coin do you have? \n" ); document.write( "
Algebra.Com's Answer #162474 by drj(1380)\"\" \"About 
You can put this solution on YOUR website!
You have 15 coins in your pocket that are either quarters or nickles. the total $2.75. how many of each coin do you have?\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let x be the number of quarters and 15-x be the number of nickles.\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let 0.25x be the cost for x number of quarters.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let 0.05(15-x) be the cost for 15-x number of nickles.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. 0.25x+0.05(15-x)=2.75 where we added Steps 1 and 2.\r
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\n" ); document.write( "\n" ); document.write( "Step 5. The following will solve the equation in Step 4.\r
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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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  • This is an equation! Solutions: x=10.
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  • Graphical form: Equation \"0.25x%2B0.05%2A%2815-x%29=2.75\" was fully solved.
  • Text form: 0.25x+0.05*(15-x)=2.75 simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+0.25x%2B0.05%2A%2815-x%29=2.75+%29\"
    For tutors: simplify_cartoon( 0.25x+0.05*(15-x)=2.75 )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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Look at \"0.25%2Ax%2B0.05%2A%28highlight_red%28+15+%29-x%29=2.75\".
Moved \"15\" to the right of expression
It becomes \"0.25%2Ax%2B0.05%2A%28-x%2Bhighlight_green%28+15+%29%29=2.75\".
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Look at \"0.25%2Ax%2B0.05%2A%28-x%2B15%29=highlight_red%28+2.75+%29\".
Moved these terms to the left \"highlight_green%28+-2.75+%29\"
It becomes \"0.25%2Ax%2B0.05%2A%28-x%2B15%29-highlight_green%28+2.75+%29=0\".
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Look at \"0.25%2Ax%2Bhighlight_red%28+0.05%2A%28-x%2B15%29+%29-2.75=0\".
Expanded term \"0.05\" by using associative property on \"%28-x%2B15%29\"
It becomes \"0.25%2Ax-highlight_green%28+0.05%2Ax+%29%2Bhighlight_green%28+0.05%2A15+%29-2.75=0\".
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Look at \"0.25%2Ax-0.05%2Ax%2Bhighlight_red%28+0.05%2A15+%29-highlight_red%28+2.75+%29=0\".
Replace constants in expression: \"highlight_red%28+0.05%2A15+%29\",\"highlight_red%28+-2.75+%29\" with \"highlight_green%28+-2+%29\"
It becomes \"highlight_green%28+-2+%29%2B0.25%2Ax-0.05%2Ax=0\".
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Look at \"highlight_red%28+-2+%29%2B0.25%2Ax-0.05%2Ax=0\".
Moved \"-2\" to the right of expression
It becomes \"0.25%2Ax-0.05%2Ax%2Bhighlight_green%28+-2+%29=0\".
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Look at \"0.25%2Ax-0.05%2Ax%2Bhighlight_red%28+-2+%29=0\".
Removed extra sign in front of \"-2\"
It becomes \"0.25%2Ax-0.05%2Ax-highlight_green%28+2+%29=0\".
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Look at \"highlight_red%28+0.25%2Ax+%29-highlight_red%28+0.05%2Ax+%29-2=0\".
Eliminated similar terms \"highlight_red%28+0.25%2Ax+%29\",\"highlight_red%28+-0.05%2Ax+%29\" replacing them with \"highlight_green%28+%280.25-0.05%29%2Ax+%29\"
It becomes \"highlight_green%28+%280.25-0.05%29%2Ax+%29-2=0\".
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Look at \"%28highlight_red%28+0.25+%29-highlight_red%28+0.05+%29%29%2Ax-2=0\".
Added fractions or integers together
It becomes \"%28highlight_green%28+20%2F100+%29%29%2Ax-2=0\".
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Look at \"highlight_red%28+%28highlight_red%28+20%2F100+%29%29%2Ax+%29-2=0\".
Remove unneeded parentheses around factor \"highlight_red%28+20+%29\",\"highlight_red%28+1%2F100+%29\"
It becomes \"highlight_green%28+20+%29%2Fhighlight_green%28+100+%29%2Ax-2=0\".
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Look at \"highlight_red%28+20+%29%2Fhighlight_red%28+100+%29%2Ax-2=0\".
Factors 20 and 100 have greatest common factor (GCF) of 20. Reducing fraction.
It becomes \"highlight_green%28+1+%29%2Fhighlight_green%28+5+%29%2Ax-2=0\".
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Look at \"highlight_red%28+1+%29%2F5%2Ax-2=0\".
Remove extraneous '1' from product \"highlight_red%28+1+%29\"
It becomes \"x%2F5-2=0\".
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Look at \"highlight_red%28+x%2F5-2+%29=0\".
Solved linear equation \"highlight_red%28+x%2F5-2=0+%29\" equivalent to 0.2*x-2 =0
It becomes \"highlight_green%28+0+%29=0\".
Result: \"0=0\"
\n" ); document.write( "This is an equation! Solutions: x=10.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "With x=10, then 10-x=5. Let's check total value 0.25*10+0.05*5=2.50+0.25=2.70 ...so it checks out.\r
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\n" ); document.write( "\n" ); document.write( "Step 6. ANSWER. The number of quarters is 10 and the number of nickels is 5.\r
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\n" ); document.write( "\n" ); document.write( "I hope the above steps were helpful. \r
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\n" ); document.write( "\n" ); document.write( "For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r
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\n" ); document.write( "\n" ); document.write( "And good luck in your studies!\r
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\n" ); document.write( "\n" ); document.write( "Respectfully,
\n" ); document.write( "Dr J\r
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