# When you subtract a 2-digit number from a 3-digit number, the difference is 473. What are the numbers?

Nov 21, 2016

$33$ and $506$.

#### Explanation:

The initial number is a 3-digit number, $x$, and the subtracted number is a 2-digit number, $y$.

Therefore,

$x - y = 473$

Plug in any two digit number for $y$, and solve for $x$. I chose $33$, my age.

$x - 33 = 473$

$x = 473 + 33$

$x = 506$

As you can see, you can use a multitude of different numbers, as long as they satisfy the requirements.

Nov 21, 2016

Assuming that the 2-digit number is positive, there are 90 possible pairs of numbers.

#### Explanation:

The positive 2-digit numbers are $10$ to $99$. (90 numbers)

he 3-digit number must be

$473 + 10$ to $473 + 99$

If a negative 2-digit number is allowed, then there are 90 more pairs

2-digit: $- 10$ $\text{ }$ to$\text{ }$ $- 99$ (90 more numbers)

3-digit: $473 + \left(- 10\right)$ $\text{ }$ to $\text{ }$ $473 + \left(- 99\right)$