How many positive two-digit integers leave a remainder of 2 when divided by 8?
I want to find all the numbers between 10 and 99 that have a remainder of 2 when divided by 8. I can use the division algorithm to write any such number as 8q + 2, where q is a quotient. The smallest value of q that makes 8q + 2 a two-digit number is 1, since 8 * 1 + 2 = 10. The largest value of q that makes 8q + 2 a two-digit number is 12, since 8 * 12 + 2 = 98. So q can range from 1 to 12, and for each value of q, I get a different number that leaves a remainder of 2 when divided by 8. Therefore, there are 12 such numbers. 