A number of students are planning an end semester party that is projected to cost $224.00. when six students decided to join in at the last minute, this reudced the contribution by $4.80 for each participanting student. how many students were there initially?
Represent the unknown:
Let x = original number of students
Let x+6 = new number of students (after six students decided to join)
It was said that the original contribution of each was reduced by $4.80 after six people joined. Thus,
(224 / x) - 4.80 = 224 / (x+6)
solving,
[(224 / x) - 4.80 = 224 / (x+6)] (x)(x+6)
224(x+6) - 4.8(x)(x+6) = 224(x)
224x + 1344 - 4.8x^2 - 28.8x = 224x
-4.8x^2 - 28.8x + 1344 = 0
x^2 + 6x - 280 = 0
Factoring,
(x + 20)(x - 14) = 0
x = -20 (extraneous root, since the number of students cannot be negative)
x = 14 students
hope this helps~ `u`