solve word problem

Question

A women group decided to raise Kshs 20000 towards a charity. Five of them were unable to contribute. The rest had to pay an extra Kshs 200 each to realize the same amount. How many members were in the group originally?      

Answer 1

The total members in the group would include the ones who paid and the five who didn't pay.  Let's call the total number x.

 

Now, the only way we can solve this is if the original plan was to have every member contribute an equal amount, which would be 20000/x per member.  If five members were unable to contribute, the group's shortfall would be 5 times 20000/x, or 100000/x.

 

If the remaining group members (totaling x-5) each paid 200 extra to make up the shortfall, that means (x-5) times 200 equals 100000/x.  Now we have an equation we can solve for x:

 

                                                                                     200(x-5) = 100000/x .  

 

Distributing on the left side, we get:                              200x - 1000 = 100000/x

 

Multiply both sides by x, and we have:                          200x² - 1000x = 100000

 

These numbers are much too big, so

let's divide everything by 200:                                        x² - 5x = 500, or 

                                                                                      x² - 5x - 500 = 0

This is an ordinary quadratic equation, and it can be

solved with your favorite method.                                  x =  (5 ± √2025)/ 2

                                                                                        = 25 or -20

since only positive answers make sense in this 

problem, the answer is 25