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A street has $50$ houses on each side, for a total of $100$ houses. The addresses on the south side of the street form an arithmetic sequence, as do the addresses on the north side of the street. On the south side, the addresses are $1,$ $5,$ $9,$ etc., and on the north side they are $3,$ $7,$ $11,$ etc. A sign painter paints house numbers on a house for $\$1$ per digit. If he paints the appropriate house number once on each of these $100$ houses, how much does he earn?

 Jul 28, 2022
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1  5  9   .....   197

3  7 11  .....   199

 

There will be   5 houses with one  digit  =  $5

 

There will be 45 houses with  two  digits =  45 (2) =  $90

 

There will be  50 houses with three  digits  = 50 (3)  = $150

 

He earns      5 + 90  + 150  =  $ 245

 

 

cool cool cool

 Jul 28, 2022

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