Question 221577
Donnie has $5.10 in nickels, dimes, and quarters.  He has an equal number of dimes and nickels, with the value of the quarters being $2.40 more than the total value of the dimes and nickels.  How many dimes does he have?


Step 1.  Let x be the number of nickels


Step 2.  Let x be the number of dimes since they are equal in number with the nickels.


Step 3.  Let {{{(0.05+0.10)x=0.15x}}} be the dollar values of nickels and dimes.


Step 4.  Let 0.25y be the dollar values of quarters.


Step 5.  {{{2.40+0.15x=0.25y}}} since the value of the quarters being $2.40 more than the total value of the dimes and nickels.  Or rewriting it as


{{{-0.15x+0.25y=2.40}}}


Step 6.  Also, {{{0.15x+0.25y=5.10}}} as given by the problem since $5.10 in nickels, dimes, and quarters.


Step 7.  Now, we have a linear system of equations in Steps 5 and 6


{{{-0.15x+0.25y=2.40}}}  Equation A
{{{0.15x+0.25y=5.10}}}   Equation B


Adding Equations A and B


{{{-0.15x+0.15x+0.25y+0.25y=2.40+5.10}}}


{{{0.50y=7.50}}}


{{{y=15}}} quarters


Then solving x from Equation B is {{{5.10-3.75=0.15x}}}  or {{{x=9}}}.


Check Equation A if true {{{-0.15x+0.25y=2.40}}} or {{{-1.35+3.75=2.40}}}...which is a true statement.


Step 8.  ANSWER:  The number of nickels and dimes is 9 each and the number of quarters is 15.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J