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# Need help, many thanks.

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There were 310 more women than men at a musical theatre. After 5/6 of the women and 3/4 of the men had left, there were 25 more women than men remaining behind. How many women were there at the musical theatre at first?

Sep 23, 2021

#1
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There were 310 more women than men at a musical theatre. After 5/6 of the women and 3/4 of the men had left, there were 25 more women than men remaining behind. How many women were there at the musical theatre at first?

Let the number of women ==W

The number og men ==310  -  W

[1/6W]  =  [1/4 *[310 - W]] +25

W==246 - Number of women originally

310  -  246 ==64 - Number of men originally.

Sep 23, 2021
#2
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Sorry, I misread the question !! I took the number of men & women ==310.

Men ==M

Women ==M + 310

1 - 5/6 ==1/6 of women remaining

1 - 3/4 ==1/4 of men remaining

1/6 * [M + 310] ==1/4M + 25, solve for M

M==320 - Number of men originally

310 + 320 ==630 - Number of women originally.

Guest Sep 23, 2021
#3
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6(x+25) - 4x = 310

2x = 310 - 150 = 160

4x + 310

= 320 +310

= 630

Sep 23, 2021