SOLUTION: James wrote several positive numbers smaller than 7 on a piece of paper. Jia then crossed out all of James's numbers and replaced each of them with their difference from 7. The sum
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-> SOLUTION: James wrote several positive numbers smaller than 7 on a piece of paper. Jia then crossed out all of James's numbers and replaced each of them with their difference from 7. The sum
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Question 1192360: James wrote several positive numbers smaller than 7 on a piece of paper. Jia then crossed out all of James's numbers and replaced each of them with their difference from 7. The sum of James' numbers was 22. The sum of Jia's numbers is 34. How many numbers did James write down? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52815) (Show Source):
Let first sum be and the second sum be .
Then + is 7 times n, where n is the number of addends in each sum.
So, the number of addends is = = 8.
ANSWER. James wrote down 8 numbers.
Apparently the other tutor misread the problem, or didn't understand it.
(Note: I see the other tutor apparently saw that her original response was incorrect and replaced it with a valid answer.)
The solution is rather simple.
For each number x that James wrote down, Jia wrote down the number (7-x); the sum of those two numbers is 7.
James's total was 22, and Jia's total was 34; that means the sum of all of their numbers was 22+34=56. Then, since the sum of each pair of numbers is 7, there must have been 56/7=8 pairs of numbers.
ANSWER: James wrote down 8 numbers.
It's easy to verify by example that the described problem CAN occur. Simply write down 8 numbers each less than 7 that have a sum of 22 to be James's numbers; then find Jia's corresponding numbers and see that their sum is 34.
