a marathon had 500 runners. each runner had a number sign attached to their chest and the numbers were 1 through 500. how many runners had a number with 1 digit on it?
Mathematics · College · Tue Nov 03 2020
Answered on
Given the statement:
A marathon had 500 runners. each runner had a number sign attached to their chest and the numbers were 1 through 500.
Determine how many runners had a numeric digit with 1 on it.
Explanation:
We can determine how many runners which contains the digit 1 on its chest by using logical analysis.
1 - 99 contains 19 runners with 1 digit on their chest.
1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, 61, 71, 81, 91
100 - 199 contains 99 runners with 1 digit on their chest
200-299 contains 19 runners with 1 digit on their chest, this is similar to 1-99.
300-399 contains 19 runners with 1 digit on their chest, this is similar to 1-99.
400 -500 contains 19 runners with 1 digit on their chest, this is similar to 1-99.
Add all the number of runners based on the logical analysis.
= 19 + 99 + 19 + 19 + 19
= 175
Final answer:
175 runners have the number 1 on their chest.