Question 578644
Let {{{ a }}} = cost of 1 donut
Let {{{ b }}} = cost of 1 lg coffee
given:
(1) {{{ 3a + 4b = 491 }}} ( in cents )
(2) {{{ 5a + 6b = 759 }}} ( in cents )
Multiply both sides of (1) by {{{ 5 }}}
Multiply both sides of (2) by {{{ 3 }}}
and subtract (2) from (1)
(1) {{{ 15a + 20b = 2455 }}}
(2) {{{ -15a - 18b = - 2277 }}}
{{{ 2b = 178 }}}
{{{ b = 89 }}}
Plug this back into (1)
(1) {{{ 3a + 4*89 = 491 }}} 
(1) {{{ 3a = 491 - 356 }}}
(1) {{{ 3a = 135 }}}
(1) {{{ a = 45 }}}
One donut costs 45 cents
One lg coffee cost 89 cents
check:
(2) {{{ 5*45 + 6*89 = 759 }}} 
(2) {{{ 225 + 534 = 759 }}}
(2) {{{ 759 = 759 }}}
OK