Can you find the number?

Question

There's a number with the following characteristics:

The hundreds digit plus the units digit minus the tens digit equals 8.
3 times the hundreds digit plus 2 times the tens digit minus the units digit equals 33.
The number divided by the sum of its digits equals 53.

What's the number?

Rand al'Thor · Accepted Answer

The number is

because we can rewrite the three given conditions as follows, where $H$, $T$, and $U$ are the hundreds, tens, and units digits respectively:

Adding the first two gives

Also from the first equation,

So the number must be

Can you find the number?

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