Question 2792: Students sent flowers costing $20 to a sick classmate. There were 4 fewer students contributing than was planned, requiring of the others to pay 25 cents more than their original share. How many students contributed to buying the flowers?
Answer by xcentaur(357)   (Show Source):
You can put this solution on YOUR website! Let the total number of students supposed to be contributing be 'x'.
Let cost of each student be M = 20/x.
Now,actual number of students contributing = (x-4).
Let actual cost of each student be N = 20/(x-4).
When there were 4 students less,they paid 25 cents more.
This means that N > M by 25 cents.
Therefore,
N-M=25 Cents or $(1/4)
Then we get,
Taking the LCM we get,
On cross multiplying we get,
Taking 320 to the other side we get,
x^2 - 4x - 320 = 0
Factorizing 320 to get a difference of 4 we get,
x^2 - 16x + 20x - 320 = 0
x(x-16) + 20(x-16) = 0
(x-16)(x+20) = 0
Then we get,
x=16 OR x=-20
As number of students cannot be negative,
x=16 is the required value of x.
Then number of students contributing is (x-4) = 12 students.
ANS: 12 students contributed.
Hope this helped,
Best of luck.
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