+142 Jo adds up all the positive integers from 1 to 100. Kate does a similar thing with the first 100 positive integers; however, she first rounds every integer to its nearest multiple of 10 (rounding 5s up) and then adds the 100 values. What is the positive difference between Jo's sum and Kate's sum?
+129852 Jo's sum is easy = (100)(101)/2 = 50 * 101 = 5050
Kate would first start with 5 [ since 1 - 4 ] are rounded to 0
Starting with 5 thru 14 she will have ten 10s
15 - 24 she will have ten 20s
25 - 34 she will have ten 30s
.
.
.
85 - 94 she will have ten 90s
95 - 100 she will have six 100s
So.....her sum is
10 [10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90] + 6 [100] =
10 [ (10) (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) ] + 6[100] =
10 (10) [ sum of the first nine positive integers ] + 6 [ 100]
100 [ (9)(10) / 2 ] + 6[100] =
100 [ 45] + 6[100] =
100 [ 45 + 6 ] =
100 [ 51 ] =
5100
So....the positive difference is 5100 - 5050 = 50
