In a two-digit number the tens’ digit is 1 more than the units’ digit. The number itself is 6 times the sum of the digits. Find the number.

Question

The answer is ???

Answer 1

A number with two digits can be written as AB where the A and the B are the digits in the tens and ones places. I set up one of the other questions you asked, I'll solve this one out in case you need to see how it's done.

 

A = B + 1

 

AB can be rewritten as 10A + B

 

10A + B = 6(A + B)

 

This gives me a system of equations. Since the first equation gives me A in terms of B, I'll replace the As in the second equation with B + 1. The first equation is saying that "A is the same thing as B + 1".

 

So dealing with the second equation:

 

10A + B = 6(A + B)

 

10(B + 1) + B = 6(B + 1 + B)

 

10B + 10 + B = 6B + 6 + 6B

 

11B + 10 = 12B + 6

 

B = 4

 

Then A is one more than this, so A = 5.

 

The number is 54.

 

(Check this: the tens digit is one more than the ones digit. Got that. When I add the digits together I get 9. If I multiply 9 by 6, I get 54.)