Question 1036213
Let {{{ c }}} = number of cats in pet store
Let {{{ d }}} = number of dogs in pet store
{{{ c/d = 2/3 }}}
(1) {{{ c = (2/3)*d }}}
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{{{ (1/4)*c + (1/2)*d = 48 }}}
multiply both sides by {{{ 4 }}}
(2) {{{ c + 2d = 192 }}}
Substitute (1) into (2)
(2) {{{ (2/3)*d + 2d = 192 }}}
(2) {{{ (8/3)*d = 192 }}}
(2) {{{ 8d = 576 }}}
(2) {{{ d = 72 }}}
and
(1) {{{ c = (2/3)*d }}}
(1) {{{ c = (2/3)*72 }}}
(1) {{{ c = 48 }}}
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{{{ c + d = 72 + 48 }}}
{{{ c + d = 120 }}}
120 animals are in the pet store
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check:
{{{ (1/4)*c + (1/2)*d = 48 }}}
{{{ (1/4)*48 + (1/2)*72 = 48 }}}
{{{ 12 + 36 = 48 }}}
{{{ 48 = 48 }}}
OK