A group of people planned to contribute equally towards a water project which needed Ksh 200,000 to complete, however, 40 members of the group without from the project. As a result, each of the remaining members was to contribute Kshs 2,500.

(a) Find the origina number of members in the group.
(b) Forty five percent of the value project was funded by Constituency Development Fund (CDF). Calculate the amount of contribution that would be made by eacg of the remaining members of the group.
(c) Members’s contributions were in terms of labour provided and money contributed. If the ratio of the value of labour to the money contributed was 6:19; calculate the total amount of money contributed by the members.

200000/2500 = 80

So, there were 120 to start with

How far do you get on the rest?

Ilunishinda

(a) Let's assume the original number of members in the group was x.

Since 40 members left the project, the remaining members would be x - 40.
Given that each remaining member needs to contribute Kshs 2,500, we can set up the following equation:
(x - 40) * 2,500 = 200,000
Simplifying the equation:
2,500x - 100,000 = 200,000
2,500x = 300,000
x = 300,000 / 2,500
x = 120
Therefore, the original number of members in the group was 120.

(b) Forty-five percent of the value of the project funded by CDF is:
0.45 * 200,000 = 90,000
The remaining amount to be contributed by the group is:
200,000 - 90,000 = 110,000
Since there are x - 40 = 120 - 40 = 80 remaining members, each member needs to contribute:
110,000 / 80 ≈ 1,375
Therefore, each of the remaining members needs to contribute approximately Kshs 1,375.

(c) Let's assume the total amount of money contributed by the members is y.
Given that the ratio of the value of labour to the money contributed is 6:19, we can set up the following equation:
6/19 = labour / y
Cross-multiplying, we get:
6y = 19 * labour
Dividing both sides by 6, we have:
y = 19/6 * labour
Since the value of labour is not given, we cannot determine the exact amount of money contributed by the members in this case.

To solve this problem, we'll break it down step by step.

(a) Let's start by finding the original number of members in the group. We know that each member was supposed to contribute equally towards the project. If the contribution per member was Ksh 2,500, we can find the number of remaining members by dividing the total amount needed for the project by the contribution per member.

Total amount needed = Ksh 200,000
Contribution per member = Ksh 2,500

Number of remaining members = Total amount needed / Contribution per member
= 200,000 / 2,500
= 80 members

But we also know that 40 members left the project. Therefore, the original number of members in the group would be:

Original number of members = Number of remaining members + Number of members who left
= 80 + 40
= 120 members

So, the original number of members in the group was 120.

(b) Now let's calculate the amount of contribution that would be made by each of the remaining members of the group. We know that 45% of the project value was funded by Constituency Development Fund (CDF). To find the remaining contribution per member, we'll subtract the CDF funding from the total amount needed and divide it by the number of remaining members.

Total amount needed = Ksh 200,000
CDF funding (45%) = 45% of Total amount needed = 0.45 * 200,000 = Ksh 90,000

Remaining amount needed = Total amount needed - CDF funding
= 200,000 - 90,000
= Ksh 110,000

Remaining contribution per member = Remaining amount needed / Number of remaining members
= 110,000 / 80
= Ksh 1,375

So, each of the remaining members of the group would contribute Ksh 1,375.

(c) Lastly, let's calculate the total amount of money contributed by the members, taking into account the ratio of the value of labor to the money contributed. We are given that the ratio of value of labor to money contributed is 6:19.

Let's assume the value of labor contributed is 6x, and the money contributed is 19x.

The total value of labor contributed can be found by multiplying the value of labor (6x) by the number of remaining members (80):

Total value of labor = Value of labor per member * Number of remaining members
= 6x * 80
= 480x

The total amount of money contributed can be found by multiplying the money contributed (19x) by the number of remaining members (80):

Total amount of money contributed = Money contributed per member * Number of remaining members
= 19x * 80
= 1520x

We know that the total amount of money contributed is equal to Ksh 110,000 (remaining amount needed):

1520x = 110,000

To solve for x, we divide both sides of the equation by 1520:

x = 110,000 / 1520
= 72.37

Now, we can calculate the total amount of money contributed:

Total amount of money contributed = Money contributed per member * Number of remaining members
= 19x * 80
= 19 * 72.37 * 80
= Ksh 109,520.80

So, the total amount of money contributed by the members is approximately Ksh 109,520.80.