SOLUTION: A group of people planned to contribute equally towards a water project which needed Sh 2,000,000 to complete. However, 40 members of the group withdrew from the project. As a resu

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Question 389381: A group of people planned to contribute equally towards a water project which needed Sh 2,000,000 to complete. However, 40 members of the group withdrew from the project. As a result, each of the remaining members were to contribute Sh 2,500 more.
a. Find the original number of members in the group.
b. 45% of the value of the project was funded by a benefactor. Calculate the amount of contribution that would be made by each remaining member of the group.
c. Members' contribution were in terms of labor provided and money contributed. If the ratio of the value of labor to the money contributed was 6:19, calculate the total amount of money contributed by the members.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the original number of members in the group
given:
2000000%2Fx is the contribution from each original member
2000000+=+%28x+-+40%29%2A%282000000%2Fx+%2B+2500%29
----------------------------------------------
2000000+=+2000000+-+80000000%2Fx+%2B+2500x+-+100000
80000000%2Fx+=+2500x+-+100000
80000000+=+2500x%5E2+-+100000x
32000+=+x%5E2+-+40x
x%5E2+-+40x+%2B+%2840%2F2%29%5E2+=+32000+%2B+%2840%2F2%29%5E2
x%5E2+-+40x+%2B+400+=+32400
%28x+-+20%29%5E2+=+180%5E2
x+-+20+=+180 (ignore the negative root)
x+=+200
(a)
There were 200 original members in the group
(b)
.45%2A2000000+=+900000
2000000+-+900000+=+1100000
1100000%2F%28200+-+40%29+=+6875
6,875 is needed from each remaining member
(c)
labor/money = 6%2F19
money/(labor + money) = 19%2F%286+%2B+19%29
money/(labor + money) = 19%2F25
1100000%2A%2819%2F25%29+=+836000
836,000 is the total amount of money contributed by the members
-----------------
check part (a)
2000000+=+%28x+-+40%29%2A%282000000%2Fx+%2B+2500%29
2000000+=+%28200+-+40%29%2A%282000000%2F200+%2B+2500%29
2000000+=+160%2A%2810000+%2B+2500%29
2000000+=+1600000+%2B+400000
2000000+=+2000000
OK