Question 760574
Let {{{ g }}} = Gary's age now
Let {{{ j }}} = Joan's age now
{{{ g + 2 }}} = Gary's age in 2 years
{{{ j + 2 }}} = Joan's age in 2 years
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(1) {{{ g = 5j }}}
(2) {{{ g + 2 = 4*( j + 2 ) }}}
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(2) {{{ g + 2 = 4j + 8 }}}
(2) {{{ g = 4j + 6 }}}
By substitution:
(2) {{{ 5j = 4j + 6 }}}
(2) {{{ j = 6 }}}
and, since
(1) {{{ g = 5j }}}
(1) {{{ g = 5*6 }}}
(1) {{{ g = 30 }}}
Joan is 6 years old
check:
(2) {{{ g + 2 = 4*( j + 2 ) }}}
(2) {{{ 30 + 2 = 4*( 6 + 2 ) }}}
(2) {{{ 32 = 4*8 }}}
(2) {{{ 32 = 32 }}}
OK