SOLUTION: Half of the cows are grazing grass .Three-fourth of the remaining are sleeping and 9 cows are drinking water from the pond.Find the total number of cows.

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Question 477893: Half of the cows are grazing grass .Three-fourth of the remaining are sleeping and 9 cows are drinking water from the pond.Find the total number of cows.
Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!

Set C as the total number of cows. Set G as the grazing cows, S as the sleeping cows, and D as the drinking cows. Set up the equation like so;


Total numbers of cows=all grazing, sleeping, and drinking cows.
C=G%2BS%2BD
Half the total cows are grazing:
G=%281%2F2%29C
Three fourths of the REMAINING cows are sleeping
S=%283%2F4%29%28C-G%29
9 cows are drinking from the pond
D=9

Plug all these answers into the original equation C=G%2BS%2BD and get C=%281%2F2%29C%2B%283%2F4%29%28C-%281%2F2%29C%29%2B9

Now simplify:
C=%281%2F2%29C%2B%283%2F8%29C%2B9
Combine all the C's on both sides:
%281%2F8%29C=9
Now multiply both sides by 8:
C=72
Answer: 72 cows
To check, plug in 72 for C.
There are 72 cows, if half of them are grazing, then 36 are grazing. If three-fourths of the rest (36 more) are sleeping, then 27 are sleeping, which leaves 9 drinking.