# Can you find the number?

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?

• You might enjoy it more if you refrain from using Wolfram Alpha. It’s not a typing puzzle. LOL – asg Jul 28 at 15:30
• (deleted my spoilery wolframalpha comment.) My point is that there isn't much puzzle to this. It's a problem in translating words to algebra, suitable for homework, not this SE. But I won't argue; at least 7 people disagree with me. – Ross Presser Jul 28 at 16:04
• I agree, it wasn't much of a challenge. That was just my first run to get my feet wet. It only took a couple of minutes to create and verify, so I didn't expect it to take too long to solve. I trust my next one will pose more of a challenge for you. BTW, my years tutoring math have convinced me that translating words into equations is a significant puzzle for many. The fact that some are very good at it does not diminish its difficulty. – asg Jul 28 at 21:40
• @RossPresser For something more challenging, try this one: puzzling.stackexchange.com/q/100599/70406 – asg Jul 31 at 2:57
• You can find the answer using the three-equations three-unknowns system too – aminabzz Aug 6 at 21:07

The number is

$$954$$,

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

$$H+U-T=8,\quad 3H+2T-U=33,\quad 100H+10T+U=53H+53T+53U$$

$$4H+T=41$$, therefore $$T=41-4H$$. Since both $$T$$ and $$H$$ must be numbers from $$0$$ to $$9$$, the only possibilities are $$H=8,T=9$$ and $$H=9,T=5$$.
$$U=8+T-H=8+(41-4H)-H=49-5H$$. Here the only possibilities are $$H=8,U=9$$ and $$H=9,U=4$$.
either $$899$$ or $$954$$. Only one of these is a multiple of $$53$$, namely $$954=53\times18=53\times(9+5+4)$$, so the problem is solved.