What is the average of all the integer values of M such that {M}/{56} is strictly between {3}/{7} and {1}/{4}?
+895 \(\frac{1}{4}<\frac{M}{56}<\frac{3}{7}\)
To do this, I would multiply everything by 56.
\((56)(\frac{1}{4})<(56)(\frac{M}{56})<(56)(\frac{3}{7})\)
56*1/4=14
56*M/56=M
56*3/7=24
\(14
All integer values of M between 14 and 24 are \(15, 16, 17, 18, 19, 20, 21, 22, 23\).
Add them all together.
\(15+16+17+18+19+20+21+22+23 = 171\)
Divide the whole thing by 9, since that is the number of terms present.
\(\frac{171}{9} = 19\)
The average is 19.
+895 \(\frac{1}{4}<\frac{M}{56}<\frac{3}{7}\)
To do this, I would multiply everything by 56.
\((56)(\frac{1}{4})<(56)(\frac{M}{56})<(56)(\frac{3}{7})\)
56*1/4=14
56*M/56=M
56*3/7=24
\(14
All integer values of M between 14 and 24 are \(15, 16, 17, 18, 19, 20, 21, 22, 23\).
Add them all together.
\(15+16+17+18+19+20+21+22+23 = 171\)
Divide the whole thing by 9, since that is the number of terms present.
\(\frac{171}{9} = 19\)
The average is 19.
