Question

In a two-digit number, the unit digit is 5 more than the tens digit. The number itself is three times the sum of the digits. What is the number?

Answer 1

27

Explanation:

You want a 2-digit number that is 3 times the sum of its digits, where the units digit is 5 more than the tens digit.

Setup

Let t represent the tens digit. Then the units digit is (t+5) and the sum of digits is ...

t +(t +5) = 2t+5

The value of the number is ...

10t +(t+5) = 11t +5

The value is 3 times the sum of digits, so we have ...

11t +5 = 3(2t +5)

Solution

11t +5 = 6t +15

5t = 10 . . . . . . . . . . subtract (6t+5)

t = 2

(t+5) = 7

The number is 27.