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  • A carpenter was hired to build 192 window frames. The first day he made five frames and each day, thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?

A carpenter was hired to build 192 window frames. The first day he made five frames and each day, thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?

Answers (1)

The first day he made 5 frames and 2 more frames each passing day. So, 

a=5 and d=2   

S_{n}= \left( \frac{n}{2} \right) \left( 2a+ \left( n-1 \right) d \right)

 

Let us assume that it takes ‘n’ days to build 192 window frames


  \\ S_{n}= \left( \frac{n}{2} \right) \left( 10+ \left( n-1 \right) 2 \right) \\\\ 192= \left( \frac{n}{2} \right) \left( 8+2n \right) \\\\ 384=2n^{2}+8n \\\\ n^{2}+4n-192=0 \\\\ \left( n-12 \right) \left( n+16 \right) =0 \\\\

Since number of days can’t be negative  n=12

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infoexpert21

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