SOLUTION: Hi The ratio of cows to sheep in farm X is 2 to 1 while that in farm Y is 3 to 1. Farm Y has twice as many cows and sheep as farm X. When 56 sheep are transferred from Y to X , th

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Hi The ratio of cows to sheep in farm X is 2 to 1 while that in farm Y is 3 to 1. Farm Y has twice as many cows and sheep as farm X. When 56 sheep are transferred from Y to X , th      Log On

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Question 1208420: Hi
The ratio of cows to sheep in farm X is 2 to 1 while that in farm Y is 3 to 1. Farm Y has twice as many cows and sheep as farm X. When 56 sheep are transferred from Y to X , the number of sheep in Y is 7/8 of the number of sheep in X.
Find the number of cows in Y.


Found 2 solutions by mccravyedwin, ikleyn:
Answer by mccravyedwin(408) About Me  (Show Source):
You can put this solution on YOUR website!
You aren't being careful with tense of English verbs.  You are using the present
tense "IS" for both the situation BEFORE the transfer of sheep and also the
situation AFTER the transfer of sheep. 

Maybe one of the other tutors will take it the way you meant it. 

Edwin

Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.
The ratio of cows to sheep in farm X is 2 to 1 while that in farm Y is 3 to 1.
Farm Y has twice as many cows and sheep altogether as farm X altogether.
When 56 sheep are transferred from Y to X , the number of sheep in Y is 7/8 of the number of sheep in X.
Find the number of cows in Y.
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        I edited your formulation by adding underlined words.

        In my opinion,  it is necessary for better understanding and to make the text unambiguous. 


Let "a" be the number of sheep in farm X.

Then the number of cows in farm X is 2a.


At farm Y, the number of sheep is "b", and the number of cows is 3b.


Farm  Y  has twice as many cows and sheep  altogether as farm  X  altogether

    b + 3b = 2(a+2a),

or

    4b = 6a.    (1)


When 56 sheep are transferred from Y to X, the number of sheep at X is (a + 56);
                                           the number of sheep at Y is (b - 56).


Now the number of sheep in Y is 7/8 of the number of sheep in X

    %287%2F8%29%2A%28a%2B56%29 = b-56.


Simplify this equation

    7(a+56) = 8*(b-56).

    7a + 392 = 2*(4b) - 448.


In the last equation, replace 4b by 6a, based on (1).  You will get

    7a + 392 = 2*(6a) - 448

    7a + 392 = 12a - 448

    392 + 448 = 12a - 7a

        840   = 5a

          a   = 840/5 = 168.


Now from (1) find  b = %286a%29%2F4 = %286%2A168%29%2F4 = 252.


ANSWER.  The number of cows in Y is  3b = 3*252 = 756.

Solved.