# 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?

Apr 18, 2016

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

#### Explanation:

This means that the value of the original number is:
$= 100 a + 10 a + \left(a + 3\right) = 111 a + 3$

The reversed number will be $b a a$, or:
$= 100 \left(a + 3\right) + 10 a + a = 111 a + 300$

Twice the original number plus 72 equals the new number:
$2 \left(111 a + 3\right) + 72 = 111 a + 300 \to$
$222 a + 78 = 111 a + 300 \to$

Subtract $111 a$ and $78$ from both sides:
$111 a = 222 \to a = 2 \to b = a + 3 = 5 \to$

The original number is $225$

$2 \times 225 + 72 = 522$, check!