Question 1018164
Let {{{ p }}} = number of pigs/5 bought
Let {{{ c }}} = number chickens/5 bought
Let {{{ s }}} = number of sheep/5 bought
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5 pigs cost $100
5 chickens cost $25
5 sheep cost $150
(1) {{{ 100/5 = 20 }}} groups of 5 animals were bought
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(1) {{{ 100p + 25c + 150s = 1000 }}}
(2) {{{ 5p + 5c + 5s = 100 }}}
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Multiply both sides of (2) by {{{ 20 }}}
and subtract (1) from (2)
(2) {{{ 100p + 100c + 100s = 2000 }}}
(1) {{{ -100p -25c - 150s = -1000 }}}
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{{{ 75c - 50s = 1000 }}}
{{{ 3c - 2s = 40 }}}
I'll try:
{{{ s = 1 }}}
{{{ c =14 }}}
{{{ 3*14 - 2*1 = 40 }}}
{{{ 42 - 2 = 40 }}}
{{{ 1 }}} = number of sheep / 5 
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There are 5 sheep
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check:
number of chickens = {{{14*5 = 70 }}}
{{{ 100 - 5 - 70 = 25 }}}
There are 25 pigs
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(1) {{{ 100p + 25c + 150s = 1000 }}}
(1) {{{ 100*5 + 25*14 + 150*1 = 1000 }}}
(1) {{{ 500 + 350 + 150 = 1000 }}}
(1) {{{ 1000 = 1000 }}}
and
(2) {{{ 5p + 5c + 5s = 100 }}}
(2) {{{ 5*5 + 5*14 + 5*1 = 100 }}}
(2) {{{ 25 + 70 + 5 = 100 }}}
(2) {{{ 100 = 100 }}}
OK