Question

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.

Answer 1

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

Answer 2

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



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