23. 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 withdrew from the project.
As a result, each of the remaining members were to contribute Ksh 2500.
(a) Find the original number of members in the group. (5 marks)
(b) Forty five percent of the value of the project was funded by Constituency Development Fund (CDF). Calculate the amount of contribution that would be made by each of the remaining members of the group. (3 marks)
(c) Member'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. (2 marks)
original number --- x
final number ------x-40
2500(x-40) = 200000
x-40 = 80
x = 120
original number = 120
remaining members = 80
b) amount that has to be paid by members = 55% of 200000
= 110000
so each remaining member must pay
110000/80 = ****
c) labour money = 6x
money = 19x
25x = ****
etc
(a) The original number of members in the group can be determined by dividing the total amount needed to complete the project by the contribution of each remaining member.
Total amount needed = Ksh 200,000
Contribution per remaining member = Ksh 2,500
Original number of members = Total amount needed / Contribution per remaining member
Original number of members = 200,000 / 2,500
Original number of members = 80
So, the original number of members in the group was 80.
(b) Forty-five percent of the project was funded by Constituency Development Fund (CDF). To find out the contribution that would be made by each remaining member, we need to subtract the CDF contribution from the total project amount and divide that by the number of remaining members.
CDF contribution = 45% of 200,000
CDF contribution = 0.45 * 200,000
CDF contribution = 90,000
Amount remaining to be contributed by the remaining members = Total amount needed - CDF contribution
Amount remaining to be contributed by the remaining members = 200,000 - 90,000
Amount remaining to be contributed by the remaining members = 110,000
Contribution per remaining member = Amount remaining to be contributed by the remaining members / Number of remaining members
Contribution per remaining member = 110,000 / 40
Contribution per remaining member = 2,750
So, each of the remaining members would contribute Ksh 2,750.
(c) The ratio of the value of labor to money contributed is 6:19. This ratio can be written as 6x:19x, where x is a common factor.
To find the total amount of money contributed by the members, we need to determine the value of 19x (money contributed).
Given that each remaining member is contributing Ksh 2,750, we can set up the following equation:
19x = 2,750
Solving for x:
x = 2,750 / 19
x ≈ 144.74
Total amount of money contributed by the members = 19x
Total amount of money contributed by the members = 19 * 144.74
Total amount of money contributed by the members ≈ Ksh 2,751.06
So, the total amount of money contributed by the members is approximately Ksh 2,751.06.
(a) To find the original number of members in the group, we can set up an equation:
Let x be the original number of members in the group.
Since each member was to contribute equally towards the project, the total amount needed is 200,000 Ksh.
After 40 members withdrew, the remaining number of members is x - 40.
Given that each remaining member was to contribute 2,500 Ksh, we can set up the 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) If 45% of the project value was funded by Constituency Development Fund (CDF), then the remaining amount to be contributed by the group members is 100% - 45% = 55%.
To calculate the amount of contribution that would be made by each of the remaining members, we can use the equation:
Amount contributed by each member = Total remaining amount / Number of remaining members
Total remaining amount = 55% of 200,000 = 0.55 * 200,000 = 110,000 Ksh
Number of remaining members = 120 - 40 = 80 members
Amount contributed by each member = 110,000 / 80 = 1,375 Ksh
Therefore, each of the remaining members of the group would contribute 1,375 Ksh.
(c) Given that the ratio of the value of labor to the money contributed is 6:19, we can set up the equation:
Value of labor / Money contributed = 6 / 19
To find the total amount of money contributed by the members, we need to find the value of each ratio part.
Let's represent the value of labor as 6x and the money contributed as 19x.
The total contribution will be the sum of the value of labor and the money contributed:
Total contribution = 6x + 19x = 25x
Given that the value of labor and money contributed is 200,000 Ksh, we can set up the equation:
25x = 200,000
x = 200,000 / 25
x = 8,000
Therefore, the total amount of money contributed by the members is:
Total contribution = 25x = 25 * 8,000 = 200,000 Ksh.
Therefore, the total amount of money contributed by the members is 200,000 Ksh.
To solve this problem, we'll break it down step by step.
(a) Find the original number of members in the group.
1. Let's assume the original number of members in the group is x.
2. Each member was supposed to contribute equally, so if there were x members, the total contribution would be x * 2500 Ksh.
3. The total contribution required to complete the project is 200,000 Ksh.
4. However, 40 members withdrew from the project, so the remaining members are (x - 40).
5. The remaining members (x - 40) now have to contribute 2500 Ksh each.
6. Therefore, we can write the equation: (x - 40) * 2500 = 200,000.
To find the value of x, we'll solve the equation:
(x - 40) * 2500 = 200,000.
Simplifying the equation:
x - 40 = 200,000 / 2500
x - 40 = 80
x = 80 + 40
x = 120
Therefore, the original number of members in the group was 120.
(b) Calculate the amount of contribution that would be made by each of the remaining members of the group.
1. We know that the remaining members of the group are (x - 40) = 120 - 40 = 80.
2. Forty-five percent of the project was funded by the Constituency Development Fund (CDF). So the remaining amount that needs to be contributed by the members is 100% - 45% = 55% of the total project cost.
3. The remaining members need to contribute equally, so the amount contributed by each member would be (55% of the project cost) / (number of remaining members).
4. Therefore, the contribution per member would be (55% of 200,000) / 80.
Calculating the amount of contribution per member:
Contribution per member = (55/100) * 200,000 / 80
Contribution per member = 110,000 / 80
Contribution per member = 1,375 Ksh
Therefore, each of the remaining members of the group needs to contribute 1,375 Ksh.
(c) Calculate the total amount of money contributed by the members.
1. We are given that the ratio of the value of labor to the money contributed is 6:19.
2. Let's assume the value of labor is 6x and the money contributed is 19x.
3. The total contribution required to complete the project is 200,000 Ksh.
4. The ratio of labor to money is 6:19, so we can write the equation: 6x + 19x = 200,000.
5. Combining like terms, we have: 25x = 200,000.
6. Dividing both sides of the equation by 25, we get: x = 200,000 / 25.
Calculating the value of x:
x = 200,000 / 25
x = 8,000
The value of money contributed by the members is 19x:
Money contributed = 19 * 8,000
Money contributed = 152,000 Ksh
Therefore, the total amount of money contributed by the members is 152,000 Ksh.