document.write( "Question 221479: Suppose you have a coin colllection of dimes and quaters containing 46 coins. if you have $6.70, how mant of each type of coin do you have? \n" ); document.write( "
Algebra.Com's Answer #166108 by drj(1380)\"\" \"About 
You can put this solution on YOUR website!
Suppose you have a coin collection of dimes and quarters containing 46 coins. if you have $6.70, how many of each type of coin do you 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 0.10x be the dollar value of dimes\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let 46-x be the number of quarters\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Let 0.25(46-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(46-x)=6.70 be the total dollar value of dimes and quarters.\r
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\n" ); document.write( "\n" ); document.write( "Step 6. The following steps will solve the equation in Step 5.\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=32.
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  • Graphical form: Equation \"0.10x%2B0.25%2A%2846-x%29=6.70\" was fully solved.
  • Text form: 0.10x+0.25*(46-x)=6.70 simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+0.10x%2B0.25%2A%2846-x%29=6.70+%29\"
    For tutors: simplify_cartoon( 0.10x+0.25*(46-x)=6.70 )
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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+46+%29-x%29=6.70\".
Moved \"46\" to the right of expression
It becomes \"0.10%2Ax%2B0.25%2A%28-x%2Bhighlight_green%28+46+%29%29=6.70\".
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Look at \"0.10%2Ax%2B0.25%2A%28-x%2B46%29=highlight_red%28+6.70+%29\".
Moved these terms to the left \"highlight_green%28+-6.70+%29\"
It becomes \"0.10%2Ax%2B0.25%2A%28-x%2B46%29-highlight_green%28+6.70+%29=0\".
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Look at \"0.10%2Ax%2Bhighlight_red%28+0.25%2A%28-x%2B46%29+%29-6.70=0\".
Expanded term \"0.25\" by using associative property on \"%28-x%2B46%29\"
It becomes \"0.10%2Ax-highlight_green%28+0.25%2Ax+%29%2Bhighlight_green%28+0.25%2A46+%29-6.70=0\".
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Look at \"0.10%2Ax-0.25%2Ax%2Bhighlight_red%28+0.25%2A46+%29-highlight_red%28+6.70+%29=0\".
Replace constants in expression: \"highlight_red%28+0.25%2A46+%29\",\"highlight_red%28+-6.70+%29\" with \"highlight_green%28+4.8+%29\"
It becomes \"highlight_green%28+4.8+%29%2B0.10%2Ax-0.25%2Ax=0\".
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Look at \"highlight_red%28+4.8+%29%2B0.10%2Ax-0.25%2Ax=0\".
Moved \"4.8\" to the right of expression
It becomes \"0.10%2Ax-0.25%2Ax%2Bhighlight_green%28+4.8+%29=0\".
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Look at \"highlight_red%28+0.10%2Ax+%29-highlight_red%28+0.25%2Ax+%29%2B4.8=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%2B4.8=0\".
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Look at \"%28highlight_red%28+0.10+%29-highlight_red%28+0.25+%29%29%2Ax%2B4.8=0\".
Added fractions or integers together
It becomes \"%28-highlight_green%28+15%2F100+%29%29%2Ax%2B4.8=0\".
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Look at \"highlight_red%28+%28-highlight_red%28+15%2F100+%29%29%2Ax+%29%2B4.8=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%2B4.8=0\".
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Look at \"-highlight_red%28+15+%29%2Fhighlight_red%28+100+%29%2Ax%2B4.8=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%2B4.8=0\".
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Look at \"highlight_red%28+-3%2F20%2Ax%2B4.8+%29=0\".
Solved linear equation \"highlight_red%28+-3%2F20%2Ax%2B4.8=0+%29\" equivalent to -0.15*x+4.8 =0
It becomes \"highlight_green%28+0+%29=0\".
Result: \"0=0\"
\n" ); document.write( "This is an equation! Solutions: x=32.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "With x=32, then 46-x=14. Check dollar value in Step 5. \r
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\n" ); document.write( "\n" ); document.write( "0.10*32+0.25*14=3.20+3.50=6.70 which is a true statement.\r
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\n" ); document.write( "\n" ); document.write( "Step 7. ANSWER: The number of dimes is 32 and the number of quarters is 14.\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 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( "Good luck in your studies!\r
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\n" ); document.write( "\n" ); document.write( "Respectfully,
\n" ); document.write( "Dr J
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