Question 938510
Let {{{ x }}} = number of $80/night rooms rented
Let {{{ y }}} = number of $120/night rooms rented
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(1) {{{ x + y = 10 }}}
(2) {{{ 80x + 120y = 920 }}}
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(2) {{{ 2x + 3y = 23 }}}
Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 2x + 3y = 23 }}}
(1) {{{ -2x - 2y = -20 }}}
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{{{ y = 3 }}}
and
(1) {{{ x + 3 = 10 }}}
(1) {{{ x = 7 }}}
7 of the $80/night rooms are rented
3 of the $120/night rooms are rented
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check:
(2) {{{ 2*7 + 3*3 = 23 }}}
(2) {{{ 14 + 9 = 23 }}}
(2) {{{ 23 = 23 }}}
OK