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.

Just work through step by step
Follow each point until you reach one answer
Digits = 7
-9 = reverse

16 - 9 = 7        x
25 - 9 = 16      x
34 - 9 = 25      x
43 - 9 = 34      Y
52 - 9 = 43      x
61 - 9 = 52      x

4 + 3 = 7
43 - 9 = 34 - the digits have been reversed

43

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

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