The sum of the digits of a two digit number is 7. If 9 is subtracted from the number, the answer will be the number with the digits reversed. Find the number.

So represent number as xy

remember that since x is in the tens place, the value of the number is 10x+y

x+y=7

if 9 is subtracted from (10x+y), then the answer will be the number with the digits reversed (10y+x)

find the number

x+y=7

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

10x+y-9=10y+x

subtract x from both sides

9x+y-9=10y

subtract y from both sides

9x-9=9y

add 9 to both sides

9x=9y+9

9 (x) = 9 (y+1)

divide both sides by 9

x=y+1

we also have x+y=7

isolate x by subtracting y from both sides

x=7-y

subsitute (7-y) for x in othe requation

7-y=y+1

add y to both sides

7=2y+1

subtract 1 from both sides

6=2y

divide both sides by 2

3=y

subsitute

x+y=7

x+3=7

subtract 3 from both sides

x=4

number=10x+y

10 (4) + 3

40+3

43

the number is 43

the number is