Please help me answer this question cos i'm going to have a math test soon...

A wealthy man sets aside a sum of money to be distributed equally among the people in a homeless shelter. As he was dividing the money, he noted that if there were 5 fewer people in the shelter, each person would have received $20 more; and if there were 4 more people in the shelter, each person would have received $10 less. How much money did the wealthy man distribute?

Stop panicking!!
money = total_money/people......................…
money + 20 = total_money/(people - 5)................(ii)
money -10 = total_money/(people + 4).................(iii)
let
m = money
t = total_money
p =people

m = t/p............................(i)
m + 20 = t/(p - 5).......................(ii)
m -10 = t/(p + 4)......................(iii)

substitute mp = t in (ii) and (iii)
m + 20 = mp/(p - 5).......................(iia)
(m+20)(p-5) =mp...........................(iib).....… both sides by (p-5)
mp +20p - 5m -100 -mp =0
20p -5m -100 = 0...........................(iic) simplifying
m -10 = mp/(p + 4)......................(iiia)
(m -10)(p+4) = mp.........................(iiib).......… both sides by (p+4)
mp -10p +4m -40 - mp =0
-10p + 4m -40 =0..........................(iiic) simplifying
-20p + 8m - 80 = 0 ........................(iiid) multiplying by 2
add (iic) and (iiid)
3m = 180
m = 60
substituting in (iic)
20p -5m -100 = 0...........................(iic)
20p - 300 = 100
20p =400
p = 20
total_money = 60 *20 =$1200
check
60 + 20 = t/(20 - 5).......................(ii)
80 = t/15
t = 1200 yes
60 -10 = t/(20 + 4)......................(iii)
50 = t/24
t = 1200 yes

Let m represent the amount of money and p represent the number of people in the shelter. We have
.. m/p = m/(p-5) - 20 = m/(p+4) + 10
.. m(p-5) = mp - 20p(p-5) ... first equation multiplied by p(p-5)
.. -5m = -20p(p-5) ... subtract mp