document.write( "Question 215524: Bonnie has twice as many dimes as quarters, and nine more nickels than quarters. The value of his coins is $2.45. How many of each kind of coin does he have? \n" ); document.write( "

Algebra.Com's Answer #162842 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
Bonnie has twice as many dimes as quarters, and nine more nickels than quarters. The value of his coins is $2.45. How many of each kind of coin does he have?\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let x be the number of quarters and 0.25x dollar value of x quarters.\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let 2x be the number of dimes and 0.10*2x=.20x dollar value of 2x dimes.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let x+9 be the number of nickels and .05(x+9)=0.05x+0.45 dollar value of x+9 nickels.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Then, total value is 0.25x+0.20x+0.05x+0.45=2.45. Solving 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=4.
Graphical form: Equation $\"0.25x%2B0.20x%2B0.05x%2B0.45=2.45\"$ was fully solved.
Text form: 0.25x+0.20x+0.05x+0.45=2.45 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+0.25x%2B0.20x%2B0.05x%2B0.45=2.45+%29\"$
For tutors: simplify_cartoon( 0.25x+0.20x+0.05x+0.45=2.45 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at

.
Eliminated similar terms $\"highlight_red%28+0.25%2Ax+%29\"$ , $\"highlight_red%28+0.20%2Ax+%29\"$ , $\"highlight_red%28+0.05%2Ax+%29\"$ replacing them with $\"highlight_green%28+%280.25%2B0.20%2B0.05%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%280.25%2B0.20%2B0.05%29%2Ax+%29%2B0.45=2.45\"$ .
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Look at

.
Added fractions or integers together
It becomes $\"%28highlight_green%28+50%2F100+%29%29%2Ax%2B0.45=2.45\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+50%2F100+%29%29%2Ax+%29%2B0.45=2.45\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+50+%29\"$ , $\"highlight_red%28+1%2F100+%29\"$
It becomes $\"highlight_green%28+50+%29%2Fhighlight_green%28+100+%29%2Ax%2B0.45=2.45\"$ .
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Look at $\"highlight_red%28+50+%29%2Fhighlight_red%28+100+%29%2Ax%2B0.45=2.45\"$ .
Factors 50 and 100 have greatest common factor (GCF) of 50. Reducing fraction.
It becomes $\"highlight_green%28+1+%29%2Fhighlight_green%28+2+%29%2Ax%2B0.45=2.45\"$ .
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Look at $\"highlight_red%28+1+%29%2F2%2Ax%2B0.45=2.45\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1+%29\"$
It becomes $\"x%2F2%2B0.45=2.45\"$ .
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Look at $\"x%2F2%2B0.45=highlight_red%28+2.45+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-2.45+%29\"$
It becomes $\"x%2F2%2B0.45-highlight_green%28+2.45+%29=0\"$ .
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Look at $\"x%2F2%2Bhighlight_red%28+0.45+%29-highlight_red%28+2.45+%29=0\"$ .
Added fractions or integers together
It becomes $\"x%2F2-highlight_green%28+200%2F100+%29=0\"$ .
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Look at $\"highlight_red%28+x%2F2-200%2F100+%29=0\"$ .
Solved linear equation $\"highlight_red%28+x%2F2-200%2F100=0+%29\"$ equivalent to 0.5*x-2 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: x=4.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "With x=4 , then 2x=8 and x+9=13\r
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\n" ); document.write( "\n" ); document.write( "Check total...4*0.25+8*0.10+13*.05=1.00+0.80+0.65=2.45 which is a true statement.\r
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\n" ); document.write( "\n" ); document.write( "Step 5. The number of quarters is 4 , the number of dimes is 8 , and the number of nickels is 13 .\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 \n" ); document.write( "

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