Problem 21, MMP

🇩🇪 Struve🇺🇲 Clagett
XXXVIII, 1Form der Berechnung des Vermischens von Opferbroten,Example of calculating the mixing of offering-bread.
2wenn man dir nennt 20 (an Zahl), gemessen (als) 1/8 Scheffel, 40 (an Zahl), gemessen (als) 1/16 Scheffel.If someone says to you: “20 measured (?) [as Horus-eye fraction] (i.e., 1/8 heqat of grain) and 40 measured (?) as [Horus-eye fraction] (i.e., 1/16 heqat of grain).”
3Berechne du 1/8 von 20, weil 1/8 Scheffel 1/8 ist.You are to take 1/8 of 20; because the [Horus-eye sign] is 1/8.
4Es entsteht 2 1/2. Berechne du 1/16 von 40, weilThe result is 2 1/2. You are to take 1/16 of 40 because
51/16 Scheffel 1/16 ist. Es entsteht 2 1/2. Berechne du[the Horus-eye sign] is 1/16. The result is 2 1/2. You are to calculate
6die Summe der beiden Hälften. Es entsteht 5. Berechne du die Summe vonthe total of these [fractions of 20 and 40]. The result is 5. You are to calculate the total
XXXIX, 1den beiden Hälften. Es entstehen 60. Dividiere du 5 durch 60.of these [initial numbers 20 and 40]. The result is 60. Then you divide 5 by 60, and
2Es entsteht 1/12 (steht 1/16). Siehe: die Mischung wird 1/12, (steht 1/16) sein. Du hast richtig gefunden.the result is 1/12 (corr. ex 1/16). Behold, the mixture is 1/12 (corr. ex 1/16). You will find [that it is] correct.

Struve:

  • x = [ ( 20 * 1/8) + 40 * 1/16 ) ] : (20 + 40)
  • 20 * 1/8 = 2 1/2
  • 40 * 1/16 = 2 1/2
  • 2 1/2 + 2 1/2 = 5
  • 40 + 20 = 60
  • 5 : 60 = 1/12

🇩🇪 Lise:

  • Information
    • b1 = 20 Broten, Type 1 (🇺🇲 loaves of bread, type 1)
    • bvbr1 = 8, Backverhältnis (🇺🇲 type 1 pefsu)
    • s1 = Scheffeln für Type 1 (🇺🇲 heqat, type 1)
    • b2 = 40 Broten, Type 2 (🇺🇲 loaves of bread, type 2)
    • bvbr2 = 16, Backverhältnis (🇺🇲 type 2 pefsu)
    • s2 = Scheffeln für Type 2 (🇺🇲 heqat, type 2)
    • vbv = Vermischte Backverhältnis (🇺🇲 mixed pefsu)
    • b1 = s1 * bvbr1
    • b2 = s2 * bvbr2
    • b1 + b2 = (s1 + s2) * vbv
  • b1 = s1 * bvbr1
  • b1 / bvbr1 = s1
  • b2 = s2 * bvbr2
  • b2 / bvbr2 = s2
  • b1 + b2 = (s1 + s2) * vbv
  • b1 + b2 = (b1 / bvbr1 + b2 / bvbr2) * vbv
  • 20 + 40 = (20 / 8 + 40 / 16) * vbv
  • 20 + 40 = (2 1/2 + 40 / 16) * vbv
  • 20 + 40 = (2 1/2 + 2 1/2) * vbv
  • 20 + 40 = 5 * vbv
  • 60 = 5 * vbv
  • 1/vbv = 5/60
  • 1/vbv = 1/12
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