Question 434075
The seating capacity can be expressed as
(number of rows)*(seats/row)
Let {{{r}}} = number of rows
Let {{{s}}} = number of seats per row
given:
(1) {{{ ( r + 4 )*( s - 2) = r*s }}}
(2) {{{ ( r - 7)*( s + 5 ) = r*s - 1 }}}
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(1) {{{ r*s + 4s - 2r - 8 = r*s }}}
(1) {{{ 4s - 2r = 8 }}}
and
(2) {{{ r*s - 7s + 5r - 35 = r*s - 1 }}}
(2) {{{ -7s + 5r = 34 }}}
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Multiply both sides of (1) by {{{5}}} and
multiply both sides of (2) by {{{2}}}
Then add the equations
(1) {{{ 20s - 10r = 40 }}}
(2) {{{ -14s + 10r = 68 }}}
{{{ 6s = 108 }}}
{{{ s = 18 }}}
and, since
(1) {{{ 4s - 2r = 8 }}}
(1) {{{ 4*18 - 2r = 8 }}}
{{{ 72 - 2r = 8 }}}
{{{ 2r = 72 - 8 }}}
{{{ 2r = 64 }}}
{{{ r = 32 }}}
Current capacity = {{{ 18*32 = 576 }}}
check:
(2) {{{ ( r - 7)*( s + 5 ) = r*s - 1 }}}
(2) {{{ ( 32 - 7)*( 18 + 5 ) = 576 - 1 }}}
{{{ 25*23 = 575 }}}
{{{ 575 = 575 }}}
OK