SOLUTION: A developmental project that was financed by an ecological organization amounted to 3.6 Million If there had been two more contributors and the expenses were shared equally, it

Question 921975: A developmental project that was financed by an ecological organization amounted to 3.6 Million If there had been two more contributors and the expenses were shared equally, it would have cost each organization 300,000 less. How many organizations contributed to the project? ( answer is 4 - show your solution )
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the project cost 3,600,000

let x = number of contributors.
let y = amount that each contributed.

you get:

y = 3,600,000 / x

if there were 2 more contributors, then the amount that each had to contribute would be 300,000 less.

you get:

y - 300,000 = 3,600,000 / (x + 2)

solve for y to get:

y = 3,600,000 / (x + 2) + 300,000

you have:

y = 3,600,000 / x

and you have:

y = 3,600,000 / (x + 2) + 300,000

since both expressions on the right side of these equation are equal to y, you can set them equal to each other to get:

3,600,000 / x = 3,600,000 / (x + 2) + 300,000

multiply both sides of this equation by x * (x + 2) and you get:

3,600,000 * (x + 2) = 3,600,000 * x + 300,000 * x * (x + 2)

divide both sides of this equation by 100,000 and you get:

36 * (x + 2) = 36 * x + 3 * x * (x + 2)

simplify by performing the indicated operations to get:

36 * x + 72 = 36 * x + 3 * x^2 + 6x

subtract 36 * x from both sides of this equation to get:

72 = 3 * x^2 + 6x

subtract 72 from both sides of this equation to get:

0 = 3 * x^2 + 6x - 72

divide both sides of this equation by 3 to get:

0 = x^2 + 2x - 24

factor this equation to get:

(x + 6) * (x - 4) = 0

solve for x to get:

x = -6 or x = 4

since x can't be negative, the only good solution is x = 4.

confirm by replacing x with 4 in your original equations to see if those equations hold true.

when x = 4, 3,600,000 / 4 = 900,000 per contributor.

when x = 6, 3,600,000 / 6 = 600,000 per contributor.

when you add two more contributors, the cost per contributor drops 300,000.

that agrees with the problem statement, so you're good.

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