Question 532754
given:
(1) {{{ a + b = 90 }}}
(2) {{{ a = (2/3)*b }}}
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(2) {{{ 3a = 2b }}}
(2) {{{ 3a - 2b = 0 }}}
Multiply both sides of (1) by {{{2}}}
and add the equations
(2) {{{ 3a - 2b = 0 }}}
(1) {{{ 2a + 2b = 180 }}}
{{{ 5a = 180 }}}
{{{ a = 36 }}}
and, since
(1) {{{ a + b = 90 }}}
(1) {{{ b = 90 - 36 }}}
(1) {{{ b = 54 }}}
The numbers are 36 and 54
check:
(2) {{{ a = (2/3)*b }}}
(2) {{{ 36 = (2/3)*54 }}}
(2) {{{ 108 = 2*54 }}}
(2) {{{ 108 = 108 }}}
OK