The sum of a 2-digit number and the 2-digit number when the digits are reversed is 77. If the difference of the same two numbers is 45, what are the two 2-digit numbers?

Number is 61 or 16

Step-by-step explanation:

Let x be the digit at tens place and y be the digit at ones place.

So, the two digit number is 10x+y.

When the digits are reversed, number becomes 10y+x

According to question,  the sum of a 2-digit number and the 2-digit number when the digits are reversed is 77

10x+y+10y+x=77

11x+11y=77

x+y=7    (i)

Also, difference of the same two numbers is 45

(10x+y)-(10y+x)=45   or   (10y+x)-(10x+y)=45

x-y=5    (ii)         or     y-x=5  (iii)

Consider equations (i) and (ii)

Put x=y+5 in x+y=7

y+5+y=7

2y=2

y=1

So, x=y+5=1+5=6

So, number = 10x+y=10(6)+1=61

Consider equations (ii) and (iii)

Put y=x+5 in x+y=7

x+5+x=7

2x=2

x=1

So, y=x+5=1+5=6

So, number = 10(1)=6=16

Therefore, number is 61 or 16