Question 721033
Let {{{ a }}} = Louise's age now
Let {{{ b }}} = Todd's age now
{{{ a - 5 }}} = Louise's age 5 yrs ago
{{{ b - 5 }}} = Todd's age 5 yrs ago
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given:
(1) {{{ a + b = 34 }}}
(2) {{{ 2*( a-5 ) + 3*( b-5 ) = 61 }}}
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(2) {{{ 2a - 10 + 3b - 15 = 61 }}}
(2) {{{ 2a + 3b = 61 + 25 }}}
(2) {{{ 2a + 3b = 86 }}}
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Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 2a + 3b = 86 }}}
(1) {{{ -2a - 2b = -68 }}}
{{{ b = 18 }}}
and, since
(1) {{{ a + b = 34 }}}
(1) {{{ a = 34 - 18 }}}
(1) {{{ a = 16 }}}
Louise's age now is 16
Todd's age now is 18
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check:
(2) {{{ 2*( a-5 ) + 3*( b-5 ) = 61 }}}
(2) {{{ 2*( 16-5 ) + 3*( 18-5 ) = 61 }}}
(2) {{{ 22 + 39 = 61 }}}
(2) {{{ 61 = 61 }}}
OK