how many three digit positive integers exist so that when divided by 7 they leave a remainder of 5 if the smallest such number is 110 and the largest 999

Question

how many integers within a certain range that leave a remainder of 5

Answer 1

We can get a rough idea by (994-105)/7=889/7=127. But 994/7=142 and 105/7=15. Subtract 14 from these and we get the range 1-128 so there are 128 integers divisible by 7 with remainder 5 between 110 and 999.

Comments

Thank you so much for your help.