Math CentralQuandaries & Queries


Question from jaydaleigh:

Mark was thinking of a number. Mark adds 11 to it, then doubles it and gets an answer of 40.5. What was the original number?


Suppose the original number was 8.6 then Mark added 11 to it to get

\[8.6 + 11.\]

Next he multiplied to get

\[2 ( 8.6 + 11).\]

Evaluating the line above gives 39.2 which is not 40.5 which is required but nevertheless the steps above show how to solve the problem you were given.

Suppose the original number was $x.$ Go through the steps above with the original number being $x$ to find an expression for Mark's answer. The value of this expression is 40.5. Solve the resulting equation for $x.$ Once you have the value of $x$ go through Mark's procedure again with this number to ensure that you obtain an answer of 40.5.

I hope this helps,

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