Question 850132
Let {{{ r }}} = number of red jelly beans
Let {{{ y }}} = number of yellow jelly beans
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If he eats 1 red, there are {{{ r -1 + y }}} remaining
(1) {{{ ( 1/7 )*( r - 1 + y ) = r - 1 }}}
If he eats 6 yellow, there are {{{ r + y - 6 }}} remaining
(2) {{{ ( 1/6 )*( r + y -5 ) = r }}}
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(1) {{{ r - 1 + y = 7*( r - 1 ) }}}
(1) {{{ r - 1 + y = 7r - 7 }}}
(1) {{{ 6r - y = 6 }}}
and
(2) {{{ r + y - 5 = 6r }}}
(2) {{{ 5r - y = -5 }}}
(2) {{{ -5r + y = 5 }}}
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Add (1) and (2)
(1) {{{ 6r - y = 6 }}}
(2) {{{ -5r + y = 5 }}}
{{{ r = 11 }}}
and
(2) {{{ -5r + y = 5 }}}
(2) {{{ -5*11 + y = 5 }}}
(2) {{{ -55 + y = 5 }}}
(2) {{{ y = 60 }}}
There are 11 red and 60 yellow
check:
If he eats 1 red, there are
70 remaining jelly beans
1/7 of 70 is 10 and there are 10 red remaining -OK
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If he eats 5 yellow, there are 66 remaining jelly beans
1/6 of 66 is 11, and that is the number of 
red remaining -OK