Question 1091830
Let {{{ q }}} = number of quarters
Let {{{ n }}} = number of nickels
--------------------------------
(1) {{{ n + q = 17 }}}
(2) {{{ 5n + 25q = 185 }}} ( in cents )
-----------------------------------
Multiply both sides of (1) by {{{5}}} and
subtract (1) fom (2)
(2) {{{ 5n + 25q = 185 }}}
(1) {{{ -5n - 5q = -85 }}}
-----------------------
{{{ 20q = 100 }}}
{{{ q = 5 }}}
and
(1) {{{ n + q = 17 }}}
(1) {{{ n + 5 = 17 }}}
(1) {{{ n = 12 }}}
---------------------
She has 5 quarters and 12 nickels
--------------------------------
check:
(2) {{{ 5*12 + 25*5 = 185 }}}
(2) {{{ 60 + 125 = 185 }}}
(2) {{{ 185 = 185 }}}
OK