Question

The sum of the digits of a 2-digit number is 7. If the digits are
reversed, the number formed is 9 less than the original number. Find
the number.
​

Answer 1

Answer:

Step-by-step explanation:

let the digits be x and y

condition(1)

x + y = 7

condition (2)

original number =10x + y

interchange number = 10y +x

now

10y + x = 10x + y - 9

9 = 10x - x +y -10y

9 = 9x - 9y

x - y =1

now solve (1) and (2)

x + y =7

x - y =1

--------

2x =8

x = 4

now sub in (1)

4 + y = 7

y = 3

the number is = 10x + y

                       -= 30 + 4

                      = 34

Answer 2

Answer:

43

Step-by-step explanation:

let's tens place = x

let's ones place = y

therefore the number willl be = 10x + y

A.T.Q

x + y = 7----- eq1

and

10y + x = (10x + y) - 9

10y -y +x-10x = -9

9y -9x = -9 -----eq2

by elimination method

eq1 * cofficent of y2. 9x +9y= 63

eq2* cofficent of y1. -9x +9y = -9

on adding both eq's. 18y = 54

now...

18y=54

y= 3

putting value of y in eq1 we get the value of y.....

eq1= x+y =7

x+(3) =7

therefore x= 4

and hence by putting the value of x and y we will get the number that is..43