Question

The sum of digits of a two digit number is 8. If the digits are reversed, the new number increased by 10 to twice the original number. Find the number.

Answer 1

Answer:

Step-by-step explanation:

Let's call the original two digit number xy, where x is the tens digit and y is the ones digit. An algebraic representation of this number is 10x + y.

The sum of the two digit number is 8: x+y=8

When the digits are reversed, the number increases by 36: (10y + x) - (10x + y) = 36

 

Now we have two equations and two unknown parameters, so we have enough information to find those parameters.

 

Solve for x:

X=8-y

 

plug in x:

(10y + 8-y) - (10(8-y)+ y) = 36

 

simplify:

(9y + 8) - (80-9y) = 36

18y - 72 = 36

y = 108/18 = 6

 

so if y=6, then x=8-y=8-6=2

 

so our number is 26. 62 is 36 greater than 26, so everything checks out.

Answer 2

Let m be the tens digit and n be the ines digit. Then the number is 10m+n

Given sum of digits is 8.
So m+n=8————-(1)

Also given that if the digits are reversed, the new number increased by 10 to twice the number.
The reversed number is 10n+m
So 10n+m=2(10m+n)+10
10n+m=20m+2n+10
8n-19m=10———-(2)

(1)x8——>
8m+8n=64————(3)
(3)-(2)——->
27m=54
m=2
Substituting the value of m in (1) we get,
n=8-m=8-2=6

So thenumber is 26.

(62=2x26 + 10)