Question 190626
"Bob has 60 coins consisting of quarters and dimes" translates to {{{d+q=60}}}. Solve for "q" to get {{{q=60-d}}}. Let's call this equation 1.


Also, "The coins combined value is $9.45" translates to {{{0.1d+0.25q=9.45}}}


Now multiply EVERY term of the last equation by 100 to make every number a whole number to get: {{{10d+25q=945}}} Let's call this equation 2.


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{{{10d+25q=945}}} Start with the second equation.



{{{10d+25(60-d)=945}}} Plug in {{{q=60-d}}}



{{{10d+1500-25d=945}}} Distribute.



{{{-15d+1500=945}}} Combine like terms on the left side.



{{{-15d=945-1500}}} Subtract {{{1500}}} from both sides.



{{{-15d=-555}}} Combine like terms on the right side.



{{{d=(-555)/(-15)}}} Divide both sides by {{{-15}}} to isolate {{{d}}}.



{{{d=37}}} Reduce.



So there are 37 dimes


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{{{q=60-d}}} Go back to the first equation



{{{q=60-37}}} Plug in {{{d=37}}}



{{{q=23}}} Subtract



So there are 23 quarters