A two digit number is 7 times the sum of its two digits. The number that is formed by reversing its digits is 18 less than the original number. What is the number?

Let me solve this step by step:

Let number be $ab$ where $a$ and $b$ are single digits.

First condition:

$10a + b = 7(a + b)$

$10a + b = 7a + 7b$

$3a - 6b = 0$

$a = 2b$ ...(1)

Second condition:

Original number = $10a + b$

Reversed number = $10b + a$

$(10a + b) - (10b + a) = 18$

$9a - 9b = 18$

$a - b = 2$ ...(2)

From (1): $a = 2b$

Substituting in (2):

$2b - b = 2$

$b = 2$

Therefore $a = 4$

Number $= 42$