Answer:
Positive difference between Jo's sum and Kate's sum = 25
Step-by-step explanation:
Jo adds up all the positive integers from 1 to 50.
Sum is given by the equation [tex]\frac{n(n+1)}{2}[/tex]
Here n = 50
Jo's sum = [tex]\frac{50(50+1)}{2}=1275[/tex]
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
