Question 521522
Let {{{d}}} = number of ducks
Let {{{g}}} = number of goats
given:
(1) {{{ d + g = 96 }}}
(2) {{{ 2d + 4g = 316 }}}
Multiply both sides of (1) by {{{2}}}
and subtract (1) from (2)
(2) {{{ 2d + 4g = 316 }}}
(1) {{{ -2d - 2g = 192 }}}
{{{ 2g = 124 }}}
{{{ g = 62 }}}
and, since
(1) {{{ d + g = 96 }}}
(1) {{{ d + 62 = 96 }}}
(1) {{{ d = 34 }}}
There are 34 ducks and 62 goats
check:
(2) {{{ 2d + 4g = 316 }}}
(2) {{{ 2*34 + 4*62 = 316 }}}
(2) {{{ 68 + 248 = 316 }}}
(2) {{{ 316 = 316 }}}
OK