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Find the average of all the integer values of $M$ such that $\frac{M}{56}$ is strictly between $\frac{1}{5}$ and $\frac{5}{4}$.

 Sep 10, 2023
 #1
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1/5 < M/56 < 5/4

 

1/5 < M /56                M/56  < 5/4

56/5 < M                   M < 56 * 5 / 4

11.2 <  M                  M < 70

 

The integer values range from  12  to  69  inclusive

 

The average of these =   sum of the  terms  /  number of terms

 

Number of terms =  69 -12 + 1 =  58

 

Sum =  (12 + 69) * (58/2) = 2349

 

Average  =   2349 / 58  =  40.5

 

 

cool cool cool

 Sep 11, 2023

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