Question

The sum of the digits of a two digit number is 8. If the digits are reversed, the new number increase by 18. Find the number​

Answer 1

Step-by-step explanation:

Let the two digit number be xy

 

x + y = 8

 

Right away I can logically see that, since the value

increases if the digits are reversed, our choices are:

17

26

35

 

If I reverse 17 I get 71 .. This is more than an 18 increase

If I reverse 26 I get 62 ... This is more than an 18 increase

If I reverse 35 I get 53... 35 + 18 = 53 so this is my answer

 

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Now algebraically:

x + y = 8   {equation 1}

 

The value of xy is 10x + y

The value of yx is 10y + x

 

10y + x = 10x + y + 18 

9y - 9x = 18

9(y - x) = 18

y - x = 2

 

From equation 1: y = 8-x

 

8 - x - x = 2

8 - 2x = 2

-2x = -6

x = 3

 

y - x = 2

y - 3 = 2

y = 5

 

Original number xy = 35

please mark my answer brainleist

Answer 2

Let the 2-digit no. Be xy

A/c to question, x+y=8......eq 1

Value of xy can be written as 10x +y

By reversing it 10y +x

Therefore,

10y+x=10x+y

9y-9x=18

Y-x=2.......eq 2

From eq 1 and 2

X+ y=8. Y-x=2

-x+y= 2. 5-x=2

Y=5 x=3