Question

The sum of the digits of a two digit number is 12. When the digits are
reversed, the difference between the new number and the original number
becomes 18. Find the original number.pls with steps

Answer 1

Answer:

Step-by-step explanation:

x+y=12

(10x+y)-(10y+x) = 18

 

From here, there are any number of possible ways to solve this system. I'll use the subtraction method, but first let's simplify equation 2:

 

x+y=12

9x-9y = 18

 

multiply both sides of equation one by 9

 

9x+9y=108

9x-9y=18

 

subtract equation two from equation one:

 

18y = 90

 

divide by 18:

 

y = 5

 

use the original first equation to find x now that we know y:

 

x + 5 = 12

x = 7

 

Now let's check that 75 actually answers the question:

 

5+7 = 12

75-57 = 18

 

So the original number is 75!