Question

In a three-digit number, the hundred’s and ten’s digit are the same. The unit’s digit is 3 more than the hundred’s digit. If the number is reversed, the new number is 72 more than twice the original number. How do you find the number?

Answer 1

So you can write the number as `aab` where `b=a+3`

Explanation:

This means that the value of the original number is:
`=100a+10a+(a+3)=111a+3`

The reversed number will be `baa`, or:
`=100(a+3)+10a+a=111a+300`

Twice the original number plus 72 equals the new number:
`2(111a+3)+72=111a+300->`
`222a+78=111a+300->`

Subtract `111a` and `78` from both sides:
`111a=222->a=2->b=a+3=5->`

The original number is `225`

Check your answer:
`2xx225+72=522`, check!