Question 885404
Let {{{ a }}} = number of 5 cent stamps
Let {{{ b }}} = number of 15 cent stamps
Let {{{ c }}} = number of 37 cent stamps
-------------------------------------
(1) {{{ a + b + c = 100 }}}
(2) {{{ 5a + 15b + 37c = 2056 }}} ( in cents )
(3) {{{ c = a + 10 }}}
-------------------
Substitute (3) into (1)
(1) {{{ a + b + a + 10 = 100 }}}
(1) {{{ 2a + b = 90 }}}
(1) {{{ b = 90 - 2a }}}
----------------------
Substitute (1) into (2)
(2) {{{ 5a + 15*( 90 - 2a ) + 37c = 2056 }}}
---------------------------------------
Substitute (3) into (2)
(2) {{{ 5a + 15*( 90 - 2a ) + 37*( a + 10 ) = 2056 }}}
(2) {{{ 5a + 1350 - 30a + 37a + 370 = 2056 }}}
(2) {{{ 12a = 2056 - 1350 - 370 }}}
(2) {{{ 12a = 2056 - 1720 }}}
(2) {{{ 12a = 336 }}}
(2) {{{ a = 28 }}}
and
(1) {{{ b = 90 - 2a }}}
(1) {{{ b = 90 - 2*28 }}}
(1) {{{ b = 34 }}}
and
(3) {{{ c = a + 10 }}}
(3) {{{ c = 38 }}}
She bought 28 of the 5 cent stamps
She bought 34 of the 15 cent stamps
She bought 38 of the 37 cent stamps
--------------------------------
check:
(2) {{{ 5a + 15b + 37c = 2056 }}} 
(2) {{{ 5*28 + 15*34 + 37*38 = 2056 }}}
(2) {{{ 140 + 510 + 1406 = 2056 }}}
(2) {{{ 2056 = 2056 }}}
OK