Question

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

Answer 1

There are actually two ways to solve this problem.

Answer 2

x+y=7

Answer 3

The first way is to derive two additional equations.
If x is the 10s digit and y is the ones digit then 10x plus y equals the number.

Answer 4

10x+y=10

Answer 5

Now, if we reverse the digits, y becomes the 10s digit and x becomes the ones digit and the number is increased by 9, so:
x+10y=n+9

Answer 6

Add -9 to both sides of this last equation to get x+10y-p=n . Now we have two things that equal n so we can set these two expressions equal to each other

Answer 7

x+10y-9=n**

Answer 8

10x+y=x+10y-9

Answer 9

9x-9y=-9

Answer 10

x-y=1

Answer 11

Add this last equation to your very first equation (x+y=7) term by term:

Answer 12

2x+0y=6

Answer 13

x=3
from 3+y=7 we get y=4 therefore the number is 34

Answer 14

oh ok thats what i got thanks!

Answer 15

np