Sounds of the Shofar

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In parshas Emor (Vayikra 23:24) we are instructed to blow the shofar on Rosh Hashonah.  On Rosh Hashana the shofar is blown with three different sounds; tekiah, shevarim and teruah.  According to most minhagim, there are 100 sounds blown before and during Musaf.  There is the same number of shevarims as teruahs.  Each set of calls begins and ends with a tekiah (or a tekiah gedolah) and there are 30 sets blown.  State the variables and write three equations for three unknowns.  Solve and determine how many of each sound is blown on each day of Rosh Hashana.

Bonus:  A tekiah is one long blast, shevarim is three medium blasts and teruah is 9 short blasts.  With the information that you found above, calculate the total number of distinct blasts of the shofar you would hear if you made it to synagogue on time both days.

The Answer:
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Let T = the number of tekiahs,  S = the number of Shevarims  R = the number of Teruahs

T + S + R = 100
S = R
T= 2 x the number of sets = 2 x 30 = 60  Substituting into the first equation:

60 + R + R = 100
60 + 2R = 100
2R = 40  So R = 20.
There are 60 Tekiahs, 20 Shevarim and 20 Teruahs.

The total number of distinct blasts for 2 days would be:
2[(1 * 60) + (3 * 20) + (9 * 20)] = 2[60 + 60 + 180] = 2[300] = 600 distinct blasts

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