Question 588435
Let {{{ c }}} = number of couples
Let {{{ s }}} = number of single persons
given:
(1) {{{ s + 2c = 180 }}}
(2) {{{ 3s + 5c = 475 }}}
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Multiply both sides of (1) by {{{3}}}
and subtract (2) from (1)
(1) {{{ 3s + 6c = 540 }}}
(2) {{{ -3s - 5c = -475 }}}
{{{ c = 65 }}}
Substitute this into (1)
(1) {{{ s + 2c = 180 }}}
(1) {{{ s + 2*65 = 180 }}}
(1) {{{ s + 130 = 180 }}}
(1) {{{ s = 50 }}}
There were 65 couples
check:
(2) {{{ 3s + 5c = 475 }}}
(2) {{{ 3*50 + 5*65 = 475 }}}
(2) {{{ 150 + 325 = 475 }}}
(2) {{{ 475 = 475 }}}
OK