There is a number,
the second digit of which is smaller than the first digit by $4$, and if the number was divided by the digits' sum, the quotient would be $7$.
What is this number.
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5
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$\begingroup$ The hint it leaves only 6 possible numbers. That is superfluous imho. $\endgroup$– Florian FCommented Jul 26, 2020 at 11:21
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$\begingroup$ @FlorianF Please tell me a better hint then. I didn't find one. $\endgroup$– math scatCommented Jul 26, 2020 at 13:43
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$\begingroup$ I would say the problem is already easy enough. No hint needed. $\endgroup$– Florian FCommented Jul 26, 2020 at 13:55
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$\begingroup$ @FlorianF Ok. edited. $\endgroup$– math scatCommented Jul 27, 2020 at 7:47
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1$\begingroup$ I think it was better to mention that the number has two digits in total. $\endgroup$– user70797Commented Aug 6, 2020 at 21:19
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2 Answers
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Here is another answer
For number AB:
1. A - B = 4
2. (10A + B) ÷ (A + B) = 7
Rearrange 1. to A = B + 4
Substitute A into 2. -> (10[B + 4] + B) ÷ ([B + 4] + B) = 7
Simplify 2.
- (10B + 40 + B) ÷ (2B + 4) = 7
- 11B + 40 = 14B + 28
- 12 = 3B
- B = 4
A = B + 4 = 8
Number is 84
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$\begingroup$ @math Thanks. How do you use the spoiler feature? $\endgroup$– asgCommented Jul 26, 2020 at 22:46
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After some guess and check, the answer is,
84
Since
8 - 4 = 4
84 / 12 = 7
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$\begingroup$ Assuming that "second digit" and "first digit" are counted from left, it is actually possible to prove that this is the unique answer, even without the hint. $\endgroup$– WhatsUpCommented Jul 25, 2020 at 18:50
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$\begingroup$ It’s an algebra problem. The answer added by @asg gives the steps. $\endgroup$– DamilaCommented Jul 26, 2020 at 5:51