Digits 1

[harpazo]

The sum of the digits of a two-digit number is 11. If we interchange the digits then the new number formed is 45 less than the original. Find the original number.

Solution:

Let x and y be the two digits.

x + y = 11
y + x = (x + y) - 45

Is this the correct set up?

 

[Mr. Bland]

Almost! For a two-digit number, one digit scales 1 and the other digit scales 10. You'll want to set up the equation like this:

[MATH]10y + x = 10x + y - 45[/MATH]​

 

[firemath]

The first part is right.

The second part-not so much.
You need not add x and y--you need them both to be in the same number.

 

[harpazo]

Almost! For a two-digit number, one digit scales 1 and the other digit scales 10. You'll want to set up the equation like this:

[MATH]10y + x = 10x + y - 45[/MATH]​

What do you mean one digit scales 1 and the other scales 10?

 

[harpazo]

The first part is right.

The second part-not so much.
You need not add x and y--you need them both to be in the same number.

Can you further explain?

 

[firemath]

What do you mean one digit scales 1 and the other scales 10?

He mean that one digit is the 10s digit and the other is the 1s digit.

 

[harpazo]

He mean that one digit is the 10s digit and the other is the 1s digit.

Ok. I got it.

 

[HallsofIvy]

For example,

31= 3(10) + 1.

94= 9(10) + 4.

 

[harpazo]

Very good.