Question 370326
You don't need to make a chart.



Since "There are 40 dimes and quarters in the drawer", we know that {{{d+q=40}}} where 'd' is the number of dimes and 'q' is the number of quarters.



Also, because "their total value was $4.75", this means that {{{0.10d+0.25q=4.75}}}



So solving the system 


{{{system(d+q=40,0.10d+0.25q=4.75)}}}


will give you the number of dimes and quarters.


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{{{0.10d+0.25q=4.75}}} Start with the second equation.



{{{10d+25q=475}}} Multiply EVERY term by 100 to make every number a whole number.



{{{d+q=40}}} Move back to the first equation.



{{{d=40-q}}} Subtract 'q' from both sides.



{{{10d+25q=475}}} Go back the to the second equation.



{{{10(40-q)+25q=475}}} Plug in {{{d=40-q}}}



{{{400-10q+25q=475}}} Distribute.



{{{15q+400=475}}} Combine like terms on the left side.



{{{15q=475-400}}} Subtract {{{400}}} from both sides.



{{{15q=75}}} Combine like terms on the right side.



{{{q=(75)/(15)}}} Divide both sides by {{{15}}} to isolate {{{q}}}.



{{{q=5}}} Reduce.



So this means that there are 5 quarters.



{{{d=40-q}}} Now move onto the equation where we've isolated 'd'.



{{{d=40-5}}} Plug in {{{q=5}}}



{{{d=35}}} Subtract



So there are 35 dimes.
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Jim