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I've been stuck on this question for a while can someone help me thanks :)

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    $\begingroup$ 65 + 7 = 72. 72/6 = 12. Reverse the operations they gave you. $\endgroup$
    – user208649
    May 29, 2015 at 17:39
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    $\begingroup$ Call the number $x$. Translate the information into an equation in $x$. Solve the equation. $\endgroup$
    – David Mitra
    May 29, 2015 at 17:42
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    $\begingroup$ Incidentally, in problems like this, if you get stuck, I recommend guessing. Obviously, it won't always solve the problem quickly, but you may get better insight into how to attack similar problems than if you just looked up how to do it. $\endgroup$
    – Brian Tung
    May 29, 2015 at 17:44
  • $\begingroup$ @BrianTung: That is terrible advice! This problem is a perfect introduction to the solution of simple equations using algebra. If you solve it by trial and error, you won't learn anything at all. And if you try to solve it by trial and error, and fail, it seems to me that you will learn less than nothing. So a lose-lose scenario. $\endgroup$
    – TonyK
    May 29, 2015 at 21:24
  • $\begingroup$ I disagree, obviously. If you just guess, and all you care about is whether you got the right answer, then yes, you are right: You don't learn anything at all. But I argue that someone who would be so remarkably uncurious as all that would never learn anything from any technique. They would only learn an isolated technique for solving one kind of problem, which is hardly any improvement at all. If you have any innate curiosity at all, you will learn from your failed attempts at guessing what analysis needs to be performed to arrive at the answer, better than if you had been told. $\endgroup$
    – Brian Tung
    May 29, 2015 at 21:49

2 Answers 2

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  1. Let $x$ equal your unknown number.
  2. Apply the operations you are given in order: $$6x - 7 = 65$$
  3. Solve for $x$ and you get your number: $$6x = 65 + 7$$ $$ 6x = 72$$ $$ x = 72/6$$ $$ x= 12$$
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$$\begin{array}{ll} \text{There is a number}&n\\ \text{if you multiply it by 6 first}&6n\\ \text{and then subtract 7 from the result}&6n-7\\ \text{you get 65}&6n-7=65 \end{array}$$

Can you take it from here?

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