document.write( "Question 103696: A box contains 140 dimes and nickles. The total value is $11.5.How many dimes and nickels are there? \n" ); document.write( "
Algebra.Com's Answer #75387 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
Let x=# of dimes, y=# of nickels\r
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\n" ); document.write( "\n" ); document.write( "So the word problem translates into this system:\r
\n" ); document.write( "\n" ); document.write( "\"x%2By=140\" \"A box contains 140 dimes and nickles\"
\n" ); document.write( "\"0.1x%2B0.05y=11.5\" \"The total value is $11.5\"\r
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\n" ); document.write( "\n" ); document.write( "\"10x%2B5y=1150\" Multiply the second equation by 100 to make every value a whole number\r
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\n" ); document.write( "\n" ); document.write( "So now we get this system:\r
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\n" ); document.write( "\n" ); document.write( "\"x%2By=140\"
\n" ); document.write( "\"10x%2B5y=1150\"\r
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Solved by pluggable solver: Solving a linear system of equations by subsitution

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\n" ); document.write( " Lets start with the given system of linear equations
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\n" ); document.write( " \"1%2Ax%2B1%2Ay=140\"
\n" ); document.write( " \"10%2Ax%2B5%2Ay=1150\"
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\n" ); document.write( " Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y.
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\n" ); document.write( " Solve for y for the first equation
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\n" ); document.write( " \"1%2Ay=140-1%2Ax\"Subtract \"1%2Ax\" from both sides
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\n" ); document.write( " \"y=%28140-1%2Ax%29\" Divide both sides by 1.
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\n" ); document.write( " Which breaks down and reduces to
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\n" ); document.write( " \"y=140-1%2Ax\" Now we've fully isolated y
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\n" ); document.write( " Since y equals \"140-1%2Ax\" we can substitute the expression \"140-1%2Ax\" into y of the 2nd equation. This will eliminate y so we can solve for x.
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\n" ); document.write( " \"10%2Ax%2B5%2Ahighlight%28%28140-1%2Ax%29%29=1150\" Replace y with \"140-1%2Ax\". Since this eliminates y, we can now solve for x.
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\n" ); document.write( " \"10%2Ax%2B5%2A%28140%29%2B5%28-1%29x=1150\" Distribute 5 to \"140-1%2Ax\"
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\n" ); document.write( " \"10%2Ax%2B700-5%2Ax=1150\" Multiply
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\n" ); document.write( " \"10%2Ax%2B700-5%2Ax=1150\" Reduce any fractions
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\n" ); document.write( " \"10%2Ax-5%2Ax=1150-700\" Subtract \"700\" from both sides
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\n" ); document.write( " \"10%2Ax-5%2Ax=450\" Combine the terms on the right side
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\n" ); document.write( " \"5%2Ax=450\" Now combine the terms on the left side.
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\n" ); document.write( " \"cross%28%281%2F5%29%285%2F1%29%29x=%28450%2F1%29%281%2F5%29\" Multiply both sides by \"1%2F5\". This will cancel out \"5%2F1\" and isolate x
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\n" ); document.write( " So when we multiply \"450%2F1\" and \"1%2F5\" (and simplify) we get
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\n" ); document.write( " \"x=90\" <---------------------------------One answer
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\n" ); document.write( " Now that we know that \"x=90\", lets substitute that in for x to solve for y
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\n" ); document.write( " \"10%2890%29%2B5%2Ay=1150\" Plug in \"x=90\" into the 2nd equation
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\n" ); document.write( " \"900%2B5%2Ay=1150\" Multiply
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\n" ); document.write( " \"5%2Ay=1150-900\"Subtract \"900\" from both sides
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\n" ); document.write( " \"5%2Ay=250\" Combine the terms on the right side
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\n" ); document.write( " \"cross%28%281%2F5%29%285%29%29%2Ay=%28250%2F1%29%281%2F5%29\" Multiply both sides by \"1%2F5\". This will cancel out 5 on the left side.
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\n" ); document.write( " \"y=250%2F5\" Multiply the terms on the right side
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\n" ); document.write( " \"y=50\" Reduce
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\n" ); document.write( " So this is the other answer
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\n" ); document.write( " \"y=50\"<---------------------------------Other answer
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\n" ); document.write( " So our solution is
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\n" ); document.write( " \"x=90\" and \"y=50\"
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\n" ); document.write( " which can also look like
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\n" ); document.write( " (\"90\",\"50\")
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\n" ); document.write( " Notice if we graph the equations (if you need help with graphing, check out this solver)
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\n" ); document.write( " \"1%2Ax%2B1%2Ay=140\"
\n" ); document.write( " \"10%2Ax%2B5%2Ay=1150\"
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\n" ); document.write( " we get
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\n" ); document.write( "
\n" ); document.write( " graph of \"1%2Ax%2B1%2Ay=140\" (red) and \"10%2Ax%2B5%2Ay=1150\" (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle.
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\n" ); document.write( " and we can see that the two equations intersect at (\"90\",\"50\"). This verifies our answer.
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\n" ); document.write( " Check:
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\n" ); document.write( " Plug in (\"90\",\"50\") into the system of equations
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\n" ); document.write( "
\n" ); document.write( " Let \"x=90\" and \"y=50\". Now plug those values into the equation \"1%2Ax%2B1%2Ay=140\"
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\n" ); document.write( " \"1%2A%2890%29%2B1%2A%2850%29=140\" Plug in \"x=90\" and \"y=50\"
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\n" ); document.write( "
\n" ); document.write( " \"90%2B50=140\" Multiply
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\n" ); document.write( " \"140=140\" Add
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\n" ); document.write( " \"140=140\" Reduce. Since this equation is true the solution works.
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\n" ); document.write( " So the solution (\"90\",\"50\") satisfies \"1%2Ax%2B1%2Ay=140\"
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\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Let \"x=90\" and \"y=50\". Now plug those values into the equation \"10%2Ax%2B5%2Ay=1150\"
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\n" ); document.write( " \"10%2A%2890%29%2B5%2A%2850%29=1150\" Plug in \"x=90\" and \"y=50\"
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\n" ); document.write( "
\n" ); document.write( " \"900%2B250=1150\" Multiply
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\n" ); document.write( " \"1150=1150\" Add
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\n" ); document.write( "
\n" ); document.write( " \"1150=1150\" Reduce. Since this equation is true the solution works.
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\n" ); document.write( "
\n" ); document.write( " So the solution (\"90\",\"50\") satisfies \"10%2Ax%2B5%2Ay=1150\"
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\n" ); document.write( "
\n" ); document.write( " Since the solution (\"90\",\"50\") satisfies the system of equations
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\n" ); document.write( "
\n" ); document.write( " \"1%2Ax%2B1%2Ay=140\"
\n" ); document.write( " \"10%2Ax%2B5%2Ay=1150\"
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\n" ); document.write( " this verifies our answer.
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "Since x=90 and y=50, this means that we have 90 dimes and 50 nickels
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