Question 1021796

let quarters be {{{q}}} and dimes {{{d}}}

if Tom has {{{21}}} coins, than 

{{{q+d=21}}}............eq.1

if totaling ${{{4.05}}}, than

{{{0.25q+0.10d=4.05}}}.........eq.2

start with
{{{q+d=21}}}............eq.1 and solve for {{{q}}}

{{{q=21-d}}}
substitute in eq.2

{{{0.25(21-d)+0.10d=4.05}}}.........eq.2,solve for {{{d}}}

{{{5.25-0.25d+0.10d=4.05}}}

{{{5.25-0.15d=4.05}}}

{{{5.25-4.05=0.15d}}}

{{{1.20=0.15d}}}

{{{d=1.20/0.15}}}

{{{d=120/15}}}

{{{highlight(d=8)}}}

go to
{{{q=21-d}}} substitute {{{8}}} for {{{d}}}

{{{q=21-8}}}

{{{highlight(q=13)}}}

so, Tom has {{{highlight(13)}}} quarters and {{{highlight(8)}}} dimes