A development project which was financed by ecological organizations amounted to P 3.6 million. If there had been two more contributors, and the expenses were shared equally, it would have cost each organization P300,000 less. How many organizations contributed to the project?
Question
A development project which was financed by ecological organizations amounted to P 3.6 million. If there had been two more contributors, and the expenses were shared equally, it would have cost each organization P300,000 less. How many organizations contributed to the project?
Solution
Let's denote the number of organizations that contributed to the project as x.
Step 1: Understand the problem The total cost of the project is P 3.6 million. If there were two more contributors (x + 2), each would have paid P300,000 less.
Step 2: Set up the equation We know that the total cost divided by the number of contributors gives the amount each contributor paid. So, we can set up the following equation:
3.6 million / x = 3.6 million / (x + 2) + 300,000
Step 3: Solve the equation To make the equation easier to solve, we can multiply all terms by x(x + 2) to get rid of the denominators:
3.6 million * (x + 2) = 3.6 million * x + 300,000 * x(x + 2)
Expanding and simplifying gives:
3.6 million * x + 7.2 million = 3.6 million * x + 300,000 * x^2 + 600,000 * x
Subtract 3.6 million * x from both sides:
7.2 million = 300,000 * x^2 + 600,000 * x
Divide all terms by 300,000:
24 = x^2 + 2x
Rearrange to standard quadratic form:
x^2 + 2x - 24 = 0
Step 4: Solve the quadratic equation The solutions to the equation are x = 4 and x = -6. Since the number of organizations can't be negative, the number of organizations that contributed to the project is 4.
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