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.