Question

sum of the digit of a two digit number 12. the given number exceeds the number obtained by interchanging the digits by 36. find the given number.​

Answer 1

Let x = the 10's digit, and y = the units digit

Write an equation for each statememt

:

"sum of the digit of two digit no. is 12."

x + y = 12

or

y = 12 - x; we use this for substitution, if needed

;

"the given no. exceed the no. obtained by interchange the digit by 36."

:

Given number: 10x + y

interchanged number: 10y + x

:

The equation from the given statement:

10x + y = 10y + x + 36

Some simple algebra:

10x - x = 10y - y + 36

9x = 9y + 36

Simplify, divide equation by 9

x = y + 4

:

Substitute (12-x) for y, (from the 1st statement)

x = (12-x) + 4

x + x = 12 + 4

2x = 16

x = 8

:

y = 12 - 8 = 4

:

Our number is 84:

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Answer 2

Answer:

12

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