jmc

Question

A two-digit integer AB equals 19 of the three-digit integer AAB, where A and B represent distinct digits from 1 to 9. What is the smallest possible value of the three-digit integer AAB?

Accepted Answer

We rewrite AB as 10A+B and AAB as 100A+10A+B. Now we set AAB=9 AB since AB is 19 of AAB. align* 100A+10A+B&=9(10A+B) &=90A+9B 20A&=8B 5A&=2B align*The smallest possible values for A and B such that 5A=2B are A=2 and B=5. So AAB=225.