SOLUTION: Hi The ratio of ducks to chickens to cows is 12 to 9 to 2 respectively. If 15 chickens were sold 4/11 of the remaining animals were chickens. What was the total number of ducks an

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Question 1205274: Hi
The ratio of ducks to chickens to cows is 12 to 9 to 2 respectively. If 15 chickens were sold 4/11 of the remaining animals were chickens. What was the total number of ducks and cows. Thanks
Answer by math_tutor2020(3816) About Me  (Show Source):
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Answer: 210

Work Shown

x = some positive integer
12x = number of ducks
9x = number of chickens
2x = number of cows

12x+9x+2x = 23x = total number of animals.

15 chickens are sold, so the chicken count drops to 9x-15 and the total drops to 23x-15

The ratio of those new counts is 4/11
(9x-15)/(23x-15) = 4/11
11(9x-15) = 4(23x-15)
99x-165 = 92x-60
99x-92x = -60+165
7x = 105
x = 105/7
x = 15

Then,
12x = 12*15 = 180 ducks
9x = 9*15 = 135 chickens
2x = 2*15 = 30 cows

There are 180+30 = 210 animals that are either a duck or a cow.

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Check:
We start off with
180 ducks
135 chickens
30 cows
That's a total of 180+135+30 = 345 animals.

We need to subtract off 15 chickens to get 135-15 = 120 chickens left.
This is out of 345-15 = 330 animals left.

Find the ratio of those new counts.
120/330 = (4*30)/(11*30) = 4/11
It shows us that the new chicken count is 4/11 of the remaining animals. We have confirmed the answer.