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James had a box of pens. He removed 1/6 of the pens and then replaced 4 pens. Next, he removed 1/4 of the remaining pens and then replaced 3 pens. Finally, he removed 1/3 of the pens that were left and replaced 2 pens. He had 46 pens in the end. How many pens did James have at first?

 Aug 23, 2021

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 #1
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Let p be the initial number of pens.

 

Number of pens after step

1.    p*5/6 + 4

 

2. (p*5/6 + 4)*3/4 + 3

 

3. [(p*5/6 +4)*3/4 + 3]*2/3 + 2 

 

So [(p*5/6 +4)*3/4 + 3]*2/3 + 2  =  46

 

Can you take it from here?

 Sep 24, 2021

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