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

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Answer 1 · 2016-11-21T07:03:00

$33$ and $506$ .

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.

Answer 2 · 2016-11-21T14:28:19

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

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: $-10$ $" "$ to $" "$ $-99$ (90 more numbers)

3-digit: $473+(-10)$ $" "$ to $" "$ $473+(-99)$