Question 401045
Let {{{a}}}  number of ants
Let {{{m}}} = number of mice
Let {{{c}}} = number of chickens
given:
(1) {{{a = 10m}}}
(2) {{{m = 4c}}}
(3) {{{6a + 4m + 2c = 1806}}}
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Substituting (2) in (1):
(1) {{{a = 10*(4c)}}}
(1) {{{a = 40c}}}
Now substitute (1) and (20 in (3):
(3) {{{6*(40c) + 4*(4c) + 2c = 1806}}}
{{{240c + 16c + 2c = 1806}}}
{{{258c = 1806}}}
{{{c = 7}}}
There are 7 chickens
check answer:
(2) {{{m = 4c}}}
{{{m = 28}}}
and
(1) {{{a = 40c}}}
{{{a = 280}}}
so,
(3) {{{6a + 4m + 2c = 1806}}}
{{{6*280 + 4*28 + 2*7 = 1806}}}
{{{1680 + 112 + 14 = 1806}}}
{{{1806 = 1806}}}
OK