Question 1112555
Let {{{ a }}} = number of beans that Mindy has to start with
Let {{{ b }}} = number of beans that Susan has to start with
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{{{ b - 80 }}} = number Susan has after {{{ 80 }}} go to Mindy
{{{ a + 80 }}} = number Mindy has after getting {{{ 80 }}} from Susan
{{{ a + 80 = b - 80 }}}
(1) {{{ -a + b = 160 }}}
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Mindy gives {{{ 20 }}} to Susan, then Mindy has
{{{ a - 20 }}}
{{{ b + 20 }}} = number Susan then has
{{{ b + 20 = 5*( a - 20 ) }}}
{{{ b + 20 = 5a - 100 }}}
(2) {{{ 5a - b = 120 }}}
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Add (1) and (2)
(1) {{{ -a + b = 160 }}}
(2) {{{ 5a - b = 120 }}}
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{{{ 4a = 280 }}}
{{{ a = 70 }}}
and
(1) {{{ -a + b = 160 }}}
(1) {{{ -70 + b = 160 }}}
(1) {{{ b = 230 }}}
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Mindy has 70 beans
and
{{{ 70 + 230 = 300 }}}
They have 300 beans together
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check:
(2) {{{ 5a - b = 120 }}}
(2) {{{ 5*70 - 230 = 120 }}}
(2) {{{ 350 - 230 = 120 }}}
(2) {{{ 120 = 120 }}}
OK