Question

Help?
The sum of the digits of a certain two digit number is 10. When you reverse the digits you increased the number by 54. what is the number?
Anyone help me with these steps?

Answer 1

x + y = 10 10x + y = (x + 10y) + 54

Answer 2

i'm confused.. can you explain the second equation?

Answer 3

If you consider x and y to be digits, then 10x will put the x in the "10"s. Same for the other side of the equation. It's just reversing. That equation comes down to:

9x - 9y = 54

x - y = 6

Answer 4

Now, you only have to solve x + y = 10 and x - y = 6

Two simultaneous equations in 2 variables.

Answer 5

let u = units digit in original number
let t = tens digit in original number

Original number:
t + u = 10

New number
10u + t = 10t + u + 54

Solve the equations as a system of equations.

Answer 6

You can take the 2nd equation and call it x = 6 - y and substitute it into the first equation and get your value for "y".

Answer 7

So,

(6 + y) + y = 10

6 + 2y = 10 -> y = 2

So, x = 8

Take a look at numbers 28 and 82 and see if they come up with the difference you are looking for.

Answer 8

82 - 28 = 54

So, these are the 2 numbers that when reversed have a diference of 54 and the digits themselves add up to 10.

Answer 9

All good now @Artchicky ?

Answer 10

not really. Still trying to understand the first part.

Answer 11

When you think of a digit, it will have a "place" in the number. If you take one of the digits, say "x", and multiply it 10, so that it is 10x, it will look like

x_

where the "-" is the "units" place and the "x" occupies the "10"s position.

It's like x-ty

Example, if your digit is 8 and you multiply it by 10, you get 80 or eighty.

Answer 12

Ohh ok i get it

Answer 13

Cool!

Answer 14

Good luck to you in all of your studies and thx for the recognition! @Artchicky

Answer 15

Thank you for your help and no problem!

Answer 16

You're very welcome! Nice working with you!