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Question 1204017: step right up and guess the number of candies in the jar three people have already guessed and their guesses are 315, 350, and 327 now here’s the big clue: one of the guesses is off by 26, one is off by 14 and one is close but off by 9 candies how many candies are in the jar?
Found 3 solutions by ikleyn, SCrappingDude, MathTherapy:
Answer by ikleyn(52864)   (Show Source):
You can put this solution on YOUR website! .
This problem was solved at this forum several/many years ago.
See the solution under this link
https://www.algebra.com/algebra/homework/Percentage-and-ratio-word-problems/Percentage-and-ratio-word-problems.faq.question.94722.html
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Notice that reasoning by @SCrappingDude are irrelevant,
since they do not give the answer to the posed question,
and even do not go in right direction.
For the safety of your mind, simply ignore the post of this person.
Answer by SCrappingDude(6)  (Show Source):
You can put this solution on YOUR website! To find the correct answer, we can start by comparing the differences between each guess and the actual number of candies. Let's calculate these differences:
1. The first guess (315) is off by 26 candies.
- If we add 26 to this guess, we get 341.
- If we subtract 26 from this guess, we get 289.
2. The second guess (350) is off by 14 candies.
- If we add 14 to this guess, we get 364.
- If we subtract 14 from this guess, we get 336.
3. The third guess (327) is close but off by 9 candies.
- If we add 9 to this guess, we get 336.
- If we subtract 9 from this guess, we get 318.
Now let's analyze the possible range of values for the number of candies based on these differences:
- The highest possible value for the number of candies would be when the first guess (315) is off by adding 26 candies, resulting in a total of 341 candies in the jar.
- The lowest possible value for the number of candies would be when the second guess (350) is off by subtracting 14 candies, resulting in a total of 336 candies in the jar.
- The closest possible value for the number of candies would be when the third guess (327) is off by adding 9 candies or subtracting 9 candies, resulting in a range of [318, 336] candies in the jar.
Considering all the given information, the number of candies in the jar can be estimated to be within the range of 318 to 341.
Answer by MathTherapy(10556)  (Show Source):
You can put this solution on YOUR website!
step right up and guess the number of candies in the jar three people have already guessed and their guesses are 315, 350, and 327 now here’s the big clue: one of the guesses is off by 26, one is off by 14 and one is close but off by 9 candies how many candies are in the jar?
What that other person wrote makes absolutely NO SENSE. I wonder if he understood what he read!
The largest number, 350, either has to be reduced or increased MINIMALLY. As such, we MUST use the
smallest difference, 9. If we reduce 350 by 9, we get 341, and if we increase 350 by 9, we get 359.
The next largest number, 327, NEEDS to be increased in order to be the same as 341 or 359. Increasing
327 to 341 requires adding 14 (341 - 327), while increasing 327 to 359 requires adding 32 (359 - 327).
We already see that, reducing 350 to 341 requires subtracting 9, and increasing 327 to 341 requires adding
14. So, so far, the match for the 1st and 2nd largest numbers is 341. Now, we have the smallest number 315
left and a difference of 26, and we KNOW, for sure, that the last and SMALLEST number, 315, needs to be
increased. We find that 315 increased by the remaining difference, 26, is in fact 341.
So, the number is DEFINITELY 341.
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