Question 896691
Instead of percents, use fractions
25% = {{{ 1/4 }}}
100% = {{{ 1 }}}
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Let {{{ a }}} = number of adults on train
Let {{{ c }}} = number of children on train
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At station A:
(1) {{{ a = c - (1/4)*c }}}
At station B:
{{{ c - 25 }}} children are left
{{{ a + 25 }}} adults on train
(2) {{{ a + 25 = c - 25 + 1*( c - 25 ) }}}
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(1) {{{ 4a = 4c - c }}}
(1) {{{ 4a = 3c }}}
(1) {{{ c = (4/3)*a }}}
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(2) {{{ a + 25 = 2c - 50 }}}
(2) {{{ a = 2c - 75 }}}
By substitution:
(2) {{{ a = 2*(4/3)*a - 75 }}}
(2) {{{ ( 8/3)*a - a = 75 }}}
(2) {{{ (5/3)*a = 75 }}}
(2) {{{ 5a = 225 }}}
(2) {{{ a = 45 }}}
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When the train left station B, there were
{{{ a + 25 = 45 + 25 }}}
{{{ a + 25 = 70 }}} adults on board
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check:
(1) {{{ a = c - (1/4)*c }}}
(1) {{{ 45 = c - (1/4)*c }}}
(1) {{{ (3/4)*c = 45 }}}
(1) {{{ c = (4/3)*45 }}}
(1) {{{ c = 60 }}}
and
(2) {{{ a + 25 = c - 25 + 1*( c - 25 ) }}}
(2) {{{ 45 + 25 = c - 25 + 1*( c - 25 ) }}}
(2) {{{ 70 = 2c - 50 }}}
(2) {{{ 2c = 120 }}}
(2) {{{ c = 60 }}}
OK