Question 624505
Let {{{ w }}} = the number of wagons
Let {{{ b }}} = the number of bikes
given:
(1) {{{ w + b = 45 }}}
(2) {{{ 4w + 2b = 100 }}}
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Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 4w + 2b = 100 }}}
(1) {{{ -2w - 2b = -90 }}}
{{{ 2w = 10 }}}
{{{ w= 5 }}}
and, since
(1) {{{ w + b = 45 }}}
(1) {{{ 5 + b = 45 }}}
(1) {{{ b = 40 }}}
There are 40 bikes and 5 wagons
check:
(2) {{{ 4*5 + 2*40 = 100 }}}
(2) {{{ 20 + 80 = 100 }}}
(2) {{{ 100 = 100 }}}