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# help plz

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What is the average of all the integer values of M such that {M}/{56} is strictly between {3}/{7} and {1}/{4}?

May 3, 2019

#1
+865
+2

$$\frac{1}{4}<\frac{M}{56}<\frac{3}{7}$$

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.

May 3, 2019

#1
+865
+2

$$\frac{1}{4}<\frac{M}{56}<\frac{3}{7}$$

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.

AdamTaurus May 3, 2019