Wat does it mean when u round every integer to its nearest multiple of 10 with the first 50 pos. integers?

Question

I have a problem, the question is....

Jo adds up all the postive integers from 1 to 50. Kate does a similar thing with the first 50 positive integers; however, she first rounds every integer to its positive difference between Jo's sum and Kate's sum?

Wat is the answer?

Answer 1

That means look at every number from 1 to 50. Round that number to the closest 10. to start 1 would round to zero as would two, three and four. Five would round to ten. 11 would round to 10 and so on.

Answer 2

The problem is with the "fives" (5, 15, 25, 35, 45).

For the tens, the difference is 0 (10 is rounded to 10, the difference is zero)

1 is rounded to 0 (difference is 1) and 9 is rounded to 10 (difference is -1). So adding 1+9 or adding 0+10 is the same.
Same thing with 2 and 8, 3 and 7, 4 and 6. The differences always cancel out. Therefore, Jo and Kate would find the same total.

Except for the "fives"
In each case, if you round up, 15 is rounded as 20 and the difference is 5. Kate's total will be greater by 5 for each "five"; there are five of them= 5*5=25

If you round down, 15 is rounded as 10 and the difference is -5. Kate's answer will be smaller by 25.

Answer 3

Jo's sum:
1 + 2 + 3 + 4 + ... + 49 + 50 = 51*50/2 = 1275

Kate's sum:
0 + 0 + 0 + 0 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 20 + 20 + 20 + ... + 40 + 40 + 40 + 40 + 50 + 50 + 50 + 50 + 50 + 50 = 0*4 + 10*10 + 20*10 + 30*10 + 40*10 + 50*6 = 1300

The positive difference is 25

Answer 4

The problem itself doesn't seem to be worded clearly to me. I would have to ask for clarification from my teacher for this problem. It's the "rounds every integer to its positive difference between Jo's sum and Kate's sum" that confuses me. I'm not sure how she would know what the difference was for her to round to in the first place. If I'm just misunderstanding the problem, then sorry.