The some of the digits ofa certain two digit number is 15 .When you reverse it’s digits increase the number by 27 . What is the number

Question

 Please help me I’m lost

Answer 1

When you have two digit number like 57, the 5 occupies the tens place and the 7 occupies the ones place. So 57 means 5·10 + 7. So if you have an unknown two digit number, xy, it means 10x + y. When you reverse the digits, yx, it means 10y + x. In the problem, when we reverse the digits, it equals the original number plus 27:

10y + x = 10x + y + 27
9y = 9x + 27
y = x + 3

The problem also tells us that the sum of the two digits is 15; that is, x + y = 15, so x = 15 - y. Let's substitute that into the y = x + 3 equation:

y = x + 3
y = 15 - y + 3
2y = 19
y = 9

x = 15 - y = 15 - 9 = 6

So the number xy = 69. Let's check, if we add 27 we should get the reverse number yx = 96:

69 + 27 = 96
96 = 96

Check!

Answer 2

When you have two digit number like 57, the 5 occupies the tens place and the 7 occupies the ones place.  So 57 means 5·10 + 7.  So if you have an unknown two digit number, xy, it means 10x + y.  When you reverse the digits, yx, it means 10y + x.  In the problem, when we reverse the digits, it equals the original number plus 27:

 

10y + x = 10x + y + 27

9y = 9x + 27

y = x + 3

 

The problem also tells us that the sum of the two digits is 15; that is, x + y = 15, so  x = 15 - y.  Let's substitute that into the y = x + 3 equation:

 

y = x + 3

y = 15 - y + 3

2y = 19

y = 9

 

x = 15 - y = 15 - 9 = 6

 

The number xy = 69.  Let's check, if we add 27 we should get the reverse number yx = 96:

 

69 + 27 = 96

96 = 96

 

Check!