Problem Solving

The ratio of men to women in the Snyder community choir is 4 to 5. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many women are in the Snyder choir?
20
24
30
32
34

Answer is C... However I solved this question using the answer choices and I got it correct also..
But can someone plz solve it for me in a proper format.. thanks..

Snyder Choir
Men=M1
Women=W1
M1/W1=4/5 or M1=4W1/5

Leigh Choir
Men=M1
Women=w2
M2/W2=5/6 or M2=5W2/6

M1-M2=4 and W1-W2=6

Substituting the value of M1 and M2 in the first eqn we have
4W1/5-5W2/6=4
Solving
24W1-25W2=120 and W1-W2=6
W1=30 and W2=24

Hence C

Ms= men in Snyder Ws= women in Snyder
Ml= men in Light Wl= women in light

Ms/Ws= 4/5 Ml/Wl=5/6

Ms=Ml+4
Ws= Wl+6 ==> Ml+4/Wl+6 = 5x+4/6x+6= 4/5
25x+20=24x+24 ==> x=4
so Ws= Wl+6= 6x+6 = 6*4+6=30

leonswati wrote:The ratio of men to women in the Snyder community choir is 4 to 5. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many women are in the Snyder choir?
20
24
30
32
34

Answer is C... However I solved this question using the answer choices and I got it correct also..
But can someone plz solve it for me in a proper format.. thanks..

In the Snyder choir, M:W = 4:5.
In the Leigh choir, M:W = 5:6.
There are 6 more women in the Snyder choir.
Thus, we need a multiple of 5 (for the Snyder choir) that is 6 more than a multiple of 6 (for the Leigh choir).

Multiples of 5 = 5,10,15,20,25,30,35,40...
Multiples of 6 = 6,12,18,24,30,36...
30-24 = 6.

To confirm:
In the Snyder choir, 4:5 = 24:30, so M=24 and W=30.
In the Leigh choir, 5:6 = 20:24, so M=20 and W=24.

Combining the choirs:
M=24+20 = 44.
W=30+24 = 54.
M:W = 44:54 = 22:27.

All the conditions are satisfied.
Thus, in the Snyder choir, W=30.

The correct answer is C.

As Sydney choir has 4 more men and 6 more women than the Leigh choir


4x-4/5x-6 = 5/6

Solving, we get x=6
Number of women in Sydney choir is 5x = 30