SOLUTION: A bag of candies was distributed equally among 16 pupils. When 7 of these pupils gave up 3/5 of their share, the rest of the pupils received 14 more candies each. How many candies
Question 1192480: A bag of candies was distributed equally among 16 pupils. When 7 of these pupils gave up 3/5 of their share, the rest of the pupils received 14 more candies each. How many candies were there in the bag? Answer by greenestamps(13206) (Show Source):
Let x be the number of candies each of the 16 students got. Then the total number of candies is 16x.
Each of 7 students gave up 3/5 of their share, which was divided equally among the other 9 students, giving each of those other students 14 more candies.
ANSWER: The number of candies in the bag was 16x = 16*30 = 480
Solving the problem using formal algebra was a good exercise, but somewhat awkward.
Solving the problem informally is better for teaching problem-solving skills -- and it provides good exercise in logical reasoning.
9 students got an additional 14 candies each; that's 9*14=126 candies.
Those 126 candies were the contributions of 7 students; the contribution from each of those 7 students was 126/7=18.
The 18 candies each of those 7 students gave up was 3/5 of their original allotment; their original allotment was 18(5/3)=30.
The 16 students originally got equal numbers of candies, so the number of candies in the bag was 30*16=480.
