Question 587059
Let the numbers be {{{a}}} and {{{b}}}
given:
(1) {{{ a + b = 19 }}}
Let {{{ b }}} = the smaller number
(2) {{{ 5b = 2a - 3 }}}
(2) {{{ b = ( 2a - 3 ) / 5 }}}
Substitute (2) into (1)
(1) {{{ a + ( 2a - 3 )/5 = 19 }}}
(1) {{{ 5a + 2a - 3 = 5*19 }}}
(1) {{{ 7a = 95 + 3 }}}
(1) {{{ 7a = 98 }}}
(1) {{{ a = 14 }}}
and, since
(1) {{{ a + b = 19 }}}
(1) {{{ 14 + b = 19 }}}
(1) {{{ b = 5 }}}
The numbers are 5 and 14
check:
(2) {{{ 5b = 2a - 3 }}}
(2) {{{ 5*5 = 2*14 - 3 }}}
(2) {{{ 25 = 28 - 3 }}}
(2) {{{ 25 = 25 }}}
OK