dave13 wrote:

Bunuel wrote:

An amount of money was divided between some people in such a way that if there had been 4 people, everyone would have $16 less. but if there had been 4 less people, everyone would have got $24 more. How many people were there in group? ?

A. 12

B. 16

C. 20

D. 24

E. 32

Bunuel you know I dont understand why i always write wrong equations when it comes to such problems. here is what i did, --- logically my approach should be correct ...

Let X be a total sum

N = number of persons

y = sum each owns after division

x / n+4 = y-16 from here follows---> x= n+4y-64

x / n-4= y+24 from here follows ---> x = n-4y-96

after this i simply got stuck

what next ?

dave13 : You're so close!

I can't tell where your calculations went wrong, but your original equations are fine.

"N" value in both of your calculations, after you set up the equations, is incorrect. See below.

Just to make it clearer, I have substituted, for X, that which equals your X: Ny (# of people * amt per person = total amt).

X = Ny. Substitute Ny for X on LHS.

First:

\(\frac{Ny}{(n+4)}\) = (y - 16)

Ny = (N + 4)(y - 16)

Ny = Ny - 16N + 4y - 64

0 = -16N + 4y - 64 (i)

Second:

\(\frac{Ny}{(n-4)}\) = y + 24

Ny = (N - 4)(y + 24)

Ny = Ny + 24N - 4y - 96

0 = 24N - 4y - 96 (ii)

Add (ii) and (i)

24N - 4y - 96

-16N + 4y - 64

-----------------

8N - 160

8N = 160

N = 20

Hope that helps.

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