Question 213532
Let {{{d}}} = number of dimes
Let {{{q}}} = number of quarters
given:
(1) {{{d + q = 26}}}
(2) {{{10d + 25q = 365}}} (in cents)
Multiply both sides of (1) by {{{10}}} 
and subtract (1) from (2)
{{{10d + 25q = 365}}} 
{{{-10d - 10q = -260}}}
{{{15q = 105}}}
{{{q = 7}}}
and, since
{{{d + q = 26}}}
{{{d + 7 = 26}}}
{{{d = 19}}}
Nancy has 19 dimes and 7 quarters
check:
(2) {{{10d + 25q = 365}}}
{{{10*19 + 25*7 = 365}}}
{{{190 + 175 = 365}}}
{{{365 = 365}}}
OK