Question 1129547
Let {{{ p }}} = number of pigeons
Let {{{ c }}} = number of cages
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(1) {{{ 5*( c-1 ) = p }}}
(2) {{{ 3c  = p - 1 }}}
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(1) {{{ 5c - 5 = p }}}
(1) {{{ 5c - p = 5 }}}
and
(2) {{{ -3c + p = 1 }}}
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Add the equations
{{{ 2c = 6 }}}
{{{ c = 3 }}}
and
(2) {{{ 3*3 = p - 1 }}}
(2) {{{ p = 10 }}}
There are 10 pigeons and 3 cages
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check:
5 pigeons in each cage is {{{ 2*5 = 10 }}} pigeons
and there is 1 cage left
3 pigeons in each cage is {{{ 3*3 = 9 }}} and 1
pigeon left makes 10 pigeons
OK