Three students Jim Rachel and Tony try to guess the number o

Three students, Jim, Rachel, and Tony, try to guess the number of beans in a jar. Jim guessed 260 beans, Rachel guessed 234 beans, and Tony guessed 274 beans. One guess was off by 9, another guess was off by 17, and the other guess was off by 31. How many beans are in the jar? Show some work.

Solution

Case 1. 234 was off by 31 ie Rachel\'s guess was off by 31

So correct number could be :201 or 265

In either case Jim\'s guess would be off by: 59 or 5 which is not possible as guesses are off by: 9,17 or 31

Case 2: 274 was off by 31 ie Tony\'s guess

So correct number could be: 305, 243

So Tony\'s guess would be off by: 45 for 305 and 17 for 243

For 243 Rachel\'s guess would be off by:9 which is again possible.

So, 243 is the required solution