Question 756514
Let {{{ n }}} = number of students
Let {{{ b }}} = number of benches
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The thing they don't mention, but is very
important is that the 8 students times the
number of benches they are seated on is
all of the students.
given:
(1) {{{ b = n/8 + 3 }}}
(2) {{{ 5b + 12 = n }}}
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(1) {{{ 8b = n + 24 }}}
(1) {{{ 8b - n = 24 }}}
and
(2) {{{ 5b + 12 = n }}}
(2) {{{ 5b - n = -12 }}}
Subtract (2) from (1)
(1) {{{ 8b - n = 24 }}}
(2) {{{ -5b + n = 12 }}}
{{{ 3b = 36 }}}
{{{ b = 12 }}}
and, since
(1) {{{ 8b - n = 24 }}}
(1) {{{ 8*12 - n = 24 }}}
(1) {{{ 96 - n = 24 }}}
(1) {{{ n = 96 - 24 }}}
(1) {{{ n = 72 }}}
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There are 72 students and 12 benches
check:
(1) {{{ b = n/8 + 3 }}}
(1) {{{ b = 72/8 + 3 }}}
(1) {{{ b = 9 + 3 }}}
(1) {{{ b = 12 }}}
and
(2) {{{ 5b + 12 = n }}}
(2) {{{ 5*12 + 12 = n }}}
(2) {{{ 60 + 12 = n }}}
(2) {{{ n = 72 }}}
OK