Question 143228
Number of dimes: {{{d}}}
Number of nickels: {{{n}}}
Value (in cents) of {{{d}}} dimes: {{{10d}}}
Value (in cents) of {{{n}}} nickels:  {{{5n}}}
Value (in cents) of current collection: {{{565}}}
Number of dimes in the 'what if' collection: {{{2d}}}
Number of nickels in the 'what if' collection: {{{n + 8}}}
Value (in cents) of the dimes in the 'what if' collection: {{{10(2d)}}}
Value (in cents) of the nickels in the 'what if' collection: {{{5(n+8)}}}
Value (in cents) of 'what if' collection: {{{1045}}}


{{{10d+5n=565}}} and
{{{10(2d)+5(n+8)=1045}}} => {{{20d+5n+40=1045}}} => {{{20d+5n=1005}}}


Now you have 2 equations in 2 variables.  Solve for d.


I changed everything from dollars/cents to cents just because I prefer integer coefficients as opposed to decimal fraction coefficients.