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There are two $2$ digits numbers. The first number is greater than $50$ and ends in $0$. When you subtract one number from the other number the difference is $29$

jameselmore
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Sophia
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2 Answers2

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Hint: Try something like $x-y = 29$ where $x = 10n, n \in \{6,7,8,9\}$

fosho
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$|a0 - bc| = 29$. $a0 > 50.$

Case 1: $a0 > bc$

so $a0 - bc = 10a - (10b + c) = 10(a - b) - c = 29 \implies c = 1; a-b = 3$. Possibilities: $(a0, [a-3]1) =\{(60, 31)(70,41)(80,51)(90,61)\}$.

Case 2: $bc > a0$

so $bc - a0 = 10b + c - 10a = 10(b-a) + c = 29 \implies c = 9; b- a = 2$. Possibilities:$ ([a+2]9, a0) = \{(89,60)(99,70)\}$

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Or if you don't like algebra.

One number is a= 60, 70, 80, or 90 and the other is $a \pm 29$. There are 8 possibilities but two of them are impossible.

fleablood
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  • Formatting...?! – fosho Jan 07 '16 at 21:32
  • What about formatting? Formatting adds nothing in this case and doesn't make anything easier to read. – fleablood Jan 07 '16 at 21:33
  • The lack of formatting here actually does make it very painful to read. – Théophile Jan 07 '16 at 21:34
  • Because it's not in italics? – fleablood Jan 07 '16 at 21:35
  • The ease of reading something that is in italics (which is all formatting adds in this case) vs. something that isn't in italics is utterly subjective. The difficulty in typing with formatting is exponentially more difficult. – fleablood Jan 07 '16 at 21:38
  • Okay, now it is formatted. You can't honestly claim that is one iota easier and less painful to read, can you? I can sure as f@@@ tell you it was a LOT more painful to type though. – fleablood Jan 07 '16 at 21:41
  • Also you should give meaning to the symbols you use, for instance $bc$ could mean $b\times c$. – fosho Jan 07 '16 at 21:42
  • Could you tone down your attitude a bit? There's no reason to be so obnoxious here. As for formatting, it isn't just about italics. As Daniel just pointed out, there's the matter of explaining what you're doing. To give one example of confusing formatting, in the first line, you've written $29.a0$, and the reader has to figure out, among other things, that there should be a space after the period and that $a0$ means $10a + 0$. – Théophile Jan 07 '16 at 21:46
  • There was a space after the period. It's disappeared because I added latex. In this case latex makes things harder. – fleablood Jan 08 '16 at 02:15
  • @fleablood I think you have a valid point, but consider that it's your effort balanced against that iota * the number of people who will ever read this answer. – Dan Brumleve Jan 08 '16 at 02:23