Question

the sum of the digits of a certain two-digits number is 7.Reversing its digits increases the number by 9.What is the number

Answer 1

Unit digit=y
tens digit=x
the number: 10x+y

We suggest this system of equations:
x+y=7
(10y+x)=(10x+y)+9
we solve it by substitution method.
x=7-y
10y+(7-y)=(10(7-y)+y)+9
9y+7=70-10y+y+9
9y+10y-y=70+9-7
18y=72
y=72/18=4

x=7-y
x=7-4=3

number=10x+y=10*3+4=30+4=34

solution: the number: 34

To check:
3+4=7
43=34+9

Answer 2

The answer is 34. 3+4=7. 43-34=9. I hope this helps.