Question 418862
Let {{{d}}} = number of dimes
Let {{{q}}} = number of quarters
given:
(1) {{{d + q = 100 }}}
(2) {{{10d + 25q = 1405 }}}
Multiply (1) by {{{10}}} and
subtract (1) from (2)
(2) {{{10d + 25q = 1405 }}} (in cents)
(1) {{{-10d - 10q = -1000 }}}
{{{ 15q = 405 }}} 
{{{q = 27 }}}
and
{{{d = 100 - q }}}
{{{d = 100 - 27 }}}
{{{d = 73 }}}
The number of dimes is 73
The number of quarters is 27
check:
(2) {{{10d + 25q = 1405 }}}
(2) {{{10*73 + 25*27 = 1405 }}}
{{{730 + 675 = 1405 }}}
{{{ 1405 = 1405 }}}
OK