document.write( "Question 227657: Jerry has 24 coins, all of which are either quarters and dimes. Their combined total equals $3.75. How many coins of each does Jerry have? \n" ); document.write( "
Algebra.Com's Answer #169095 by drj(1380)\"\" \"About 
You can put this solution on YOUR website!
Jerry has 24 coins, all of which are either quarters and dimes. Their combined total equals $3.75. How many coins of each does Jerry have?\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let x be the number of dimes\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let 24-x be the number of quarters since there are 16 coins in all.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let 0.10x be the dollar value of dimes.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Let 0.25(24-x) be the dollar value of quarters.\r
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\n" ); document.write( "\n" ); document.write( "Step 5. Then, 0.10x+0.25(24-x)=3.75 be the total dollar value of 3.75.\r
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\n" ); document.write( "\n" ); document.write( "Step 6. Solving the equation in Step 5 yields the following steps:\r
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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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


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  • This is an equation! Solutions: x=15.
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  • Graphical form: Equation \"0.10x%2B0.25%2A%2824-x%29=3.75\" was fully solved.
  • Text form: 0.10x+0.25*(24-x)=3.75 simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+0.10x%2B0.25%2A%2824-x%29=3.75+%29\"
    For tutors: simplify_cartoon( 0.10x+0.25*(24-x)=3.75 )
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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 \"0.10%2Ax%2B0.25%2A%28highlight_red%28+24+%29-x%29=3.75\".
Moved \"24\" to the right of expression
It becomes \"0.10%2Ax%2B0.25%2A%28-x%2Bhighlight_green%28+24+%29%29=3.75\".
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Look at \"0.10%2Ax%2B0.25%2A%28-x%2B24%29=highlight_red%28+3.75+%29\".
Moved these terms to the left \"highlight_green%28+-3.75+%29\"
It becomes \"0.10%2Ax%2B0.25%2A%28-x%2B24%29-highlight_green%28+3.75+%29=0\".
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Look at \"0.10%2Ax%2Bhighlight_red%28+0.25%2A%28-x%2B24%29+%29-3.75=0\".
Expanded term \"0.25\" by using associative property on \"%28-x%2B24%29\"
It becomes \"0.10%2Ax-highlight_green%28+0.25%2Ax+%29%2Bhighlight_green%28+0.25%2A24+%29-3.75=0\".
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Look at \"0.10%2Ax-0.25%2Ax%2Bhighlight_red%28+0.25%2A24+%29-highlight_red%28+3.75+%29=0\".
Replace constants in expression: \"highlight_red%28+0.25%2A24+%29\",\"highlight_red%28+-3.75+%29\" with \"highlight_green%28+2.25+%29\"
It becomes \"highlight_green%28+2.25+%29%2B0.10%2Ax-0.25%2Ax=0\".
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Look at \"highlight_red%28+2.25+%29%2B0.10%2Ax-0.25%2Ax=0\".
Moved \"2.25\" to the right of expression
It becomes \"0.10%2Ax-0.25%2Ax%2Bhighlight_green%28+2.25+%29=0\".
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Look at \"highlight_red%28+0.10%2Ax+%29-highlight_red%28+0.25%2Ax+%29%2B2.25=0\".
Eliminated similar terms \"highlight_red%28+0.10%2Ax+%29\",\"highlight_red%28+-0.25%2Ax+%29\" replacing them with \"highlight_green%28+%280.10-0.25%29%2Ax+%29\"
It becomes \"highlight_green%28+%280.10-0.25%29%2Ax+%29%2B2.25=0\".
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Look at \"%28highlight_red%28+0.10+%29-highlight_red%28+0.25+%29%29%2Ax%2B2.25=0\".
Added fractions or integers together
It becomes \"%28-highlight_green%28+15%2F100+%29%29%2Ax%2B2.25=0\".
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Look at \"highlight_red%28+%28-highlight_red%28+15%2F100+%29%29%2Ax+%29%2B2.25=0\".
Remove unneeded parentheses around factor \"highlight_red%28+15+%29\",\"highlight_red%28+1%2F100+%29\"
It becomes \"-highlight_green%28+15+%29%2Fhighlight_green%28+100+%29%2Ax%2B2.25=0\".
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Look at \"-highlight_red%28+15+%29%2Fhighlight_red%28+100+%29%2Ax%2B2.25=0\".
Factors 15 and 100 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes \"-highlight_green%28+3+%29%2Fhighlight_green%28+20+%29%2Ax%2B2.25=0\".
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Look at \"highlight_red%28+-3%2F20%2Ax%2B2.25+%29=0\".
Solved linear equation \"highlight_red%28+-3%2F20%2Ax%2B2.25=0+%29\" equivalent to -0.15*x+2.25 =0
It becomes \"highlight_green%28+0+%29=0\".
Result: \"0=0\"
\n" ); document.write( "This is an equation! Solutions: x=15.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "With x=15 then 24-x=9\r
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\n" ); document.write( "\n" ); document.write( "Check the total dollar value 0.10*15 + 0.25*9 =1.50+2.25=3.75 which is a true statement.\r
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\n" ); document.write( "\n" ); document.write( "Step 7. ANSWER: The number of dimes is 15 and the number of quarters is 9.\r
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\n" ); document.write( "\n" ); document.write( "I hope the above steps and explanation were helpful.\r
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\n" ); document.write( "\n" ); document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and 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
\n" ); document.write( "\n" ); document.write( "http://www.FreedomUniversity.TV
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