The sum of the digits of a two-digit number is 12. The number formed by interchanging the digits is 54 more than the original number. What is the original number? 39 48 57

Step-by-step explanation: Given that the sum of the digits of a two-digit number is 12 and the number formed by interchanging the digits is 54 more than the original numbers. We are to find the original number.

Let (10x + y) be the original number.

According to the given information, we have

[tex]x+y=12,~~~~~~~~~~~~~~~(A)\\\\(10y+x)-(10x+y)=54\\\\\Rightarrow 9y-9x=54\\\\\Rightarrow y-x=6.~~~~~~~~~~~~~(B)[/tex]

Adding the equations (A) and (B), we have

[tex]2y=18\\\\\Rightarrow y=9,[/tex]

and

[tex]x=12-9=3.[/tex]

Thus, the number is (10 × 3 + 9) = 39.

facundo3141592 facundo3141592 · Answer 2 · 2019-11-08T16:09:27+01:00

Answer: Hello there!

The sum of the two digits is 12; let's wich options make this true:

39) 3 + 9 = 12

48 ) 4 + 8 = 12

57 ) 5 + 7 = 12

So the 3 options still are possible solutions.

Now "the number formed by interchanging the digits is 54 more than the original number"

let's see wich option makes this true:

39) the interchange of 39 is 93, and the difference is 93 - 39 = 54

So 39 is a solution of this problem let's see the other options.

48) the inverse is 84, and the difference between both numbers is 84 - 48 = 36, this is not a solution of the proble,

57) the inverse is 75, and the difference between both numbers is 75 - 57 = 18, this is not a solution

So the original number is 39.