Sum of the digits of a two digit no.is 12 . The given no. exceed s the no. obtained by interchanging the digits by 36. Find the given no.
Answers & Comments
Anmol18125
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: : : Check it: 84 - 48 = 36
Answers & Comments
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:
:
:
Check it: 84 - 48 = 36
I hope u understand