Question

Jo adds up all the positive integers from 1 to 50. Kate does a similar thing with the first 50 positive integers; however, she first rounds every integer to its nearest multiple of 10 (rounding 5s up) and then adds the 50 values. What is the positive difference between Jo's sum and Kate's sum?

Answer 1

25

Explanation:

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Answer 2

Positive difference between Jo's sum and Kate's sum = 25

Explanation:

Jo adds up all the positive integers from 1 to 50.

Sum is given by the equation
`(n(n+1))/(2)`

Here n = 50

Jo's sum =
`(50(50+1))/(2)=1275`

Kate does a similar thing with the first 50 positive integers; however, she first rounds every integer to its nearest multiple of 10 (rounding 5s up) and then adds the 50 values.

1 to 4 will be rounded to 0 ( Total 4 zeros)

5 to 14 will be rounded to 10 ( Total 10 tens)

15 to 24 will be rounded to 20 ( Total 10 twenties)

25 to 34 will be rounded to 30 ( Total 10 thirties)

35 to 44 will be rounded to 40 ( Total 10 forties)

45 to 50 will be rounded to 50 ( Total 6 fifties)

Kate's sum = 4 x 0 + 10 x 10 + 10 x 20 + 10 x 30 + 10 x 40 + 6 x 50 = 1300

Positive difference between Jo's sum and Kate's sum = 1300 - 1275 = 25