SOLUTION: there are 10 times more ants than mice and 4 times more mice than chickens. All together they have 1,806 feet. How many chickens are there? Please show all work

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Question 401045: there are 10 times more ants than mice and 4 times more mice than chickens. All together they have 1,806 feet. How many chickens are there?
Please show all work

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a number of ants
Let m = number of mice
Let c = number of chickens
given:
(1) a+=+10m
(2) m+=+4c
(3) 6a+%2B+4m+%2B+2c+=+1806
----------------------------------
Substituting (2) in (1):
(1) a+=+10%2A%284c%29
(1) a+=+40c
Now substitute (1) and (20 in (3):
(3) 6%2A%2840c%29+%2B+4%2A%284c%29+%2B+2c+=+1806
240c+%2B+16c+%2B+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+%2B+4m+%2B+2c+=+1806
6%2A280+%2B+4%2A28+%2B+2%2A7+=+1806
1680+%2B+112+%2B+14+=+1806
1806+=+1806
OK