The sum of the digits of a two-digit number is 8. If the digits are interchanged ,new number is 10 more than double the original number. Find the original number. pls help me I want ans with full process

Original number 26.

Step-by-step explanation:

xy - two-digit number

1) x + y = 8

2) Original two-digit number can be written as

10*x + y

3) If the digits interchanged yx,

then the new number can be written as

10*y + x

4)  Double the original number is

2*(10*x + y)

5) New number is 10 more than double the original number

(10*y + x) - (2*(10*x + y)) = 10

6) Now we have the system of 2 equations:

x + y = 8

(10*y + x) - (2*(10*x + y)) = 10 > 10y + x - (20x + 2y) = 10 ---> 8y - 19x = 10

x = 8 - y

8y - 19(8 - y) = 10

8y - 152 +19y = 10

27y = 162

y = 6

x = 8 - y = 8 - 6 = 2

x = 2

So, x =2, y = 6.

Original number 26.

Check:

Original number 26.

New number 62.

Double of the original number = 2*26= 52.

New number is 10 more than double the original number :

62 - 52 = 10 True

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