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Gib die Lösung in \( l \) an: \( (472.6 l: 17)-88.75 d l+\square=\left(5 \frac{7}{8} l \cdot 24\right) \)

Ask by Bradley Stuart. in Switzerland
Feb 24,2025

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Answer

Der fehlende Term □ beträgt 122,075 Liter.

Solution

Wir interpretieren die Einheiten folgendermaßen: • l steht für Liter. • dl steht für Deziliter, wobei 1 l = 10 dl. Gegeben ist die Gleichung   (472,6 l : 17) – 88,75 dl + □ = (5 7/8 l · 24). Schritt 1. Berechne den ersten Term:   472,6 l geteilt durch 17:    472,6 ÷ 17 = 27,8 ⇒ 27,8 l Schritt 2. Wandeln Sie 88,75 dl in Liter um:   88,75 dl = 88,75 ÷ 10 = 8,875 l Schritt 3. Setzen Sie die umgerechneten Terme in die Gleichung ein:   27,8 l – 8,875 l + □ = (5 7/8 l) · 24 Berechnen Sie zuerst die linke Seite:   27,8 l – 8,875 l = 18,925 l Schritt 4. Bestimmen Sie den rechten Term. Der Ausdruck 5 7/8 l kann in einen unechten Bruch umgerechnet werden:   5 7/8 = (5·8 + 7)/8 = (40 + 7)/8 = 47/8. Multipliziert mit 24 erhält man:   (47/8 l) · 24 = 47 · 3 l = 141 l Schritt 5. Stellen Sie die Gleichung um, um □ zu isolieren:   18,925 l + □ = 141 l   □ = 141 l – 18,925 l = 122,075 l Ergebnis: Der fehlende Term □ beträgt 122,075 l (gerundet kann man auch 122,08 l angeben).

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Um die Lösung für die Gleichung zu finden, beginnen wir mit der Umformung der Gleichung. Zuerst berechnen wir den rechten Teil: \[ 5 \frac{7}{8} l \cdot 24 = \left(\frac{47}{8} l \cdot 24\right) = \frac{1128}{8} l = 141 l \] Setzen wir diese Berechnung in die Gleichung ein: \[ (472.6 l : 17) - 88.75 d l + \square = 141 l \] Berechnen wir nun \( 472.6 l : 17 \): \[ 472.6 l : 17 = 27.8 l \] Jetzt setzen wir das in die Gleichung ein: \[ 27.8 l - 88.75 d l + \square = 141 l \] Um \(\square\) zu isolieren, bringen wir die anderen Terme auf die andere Seite: \[ \square = 141 l - 27.8 l + 88.75 d l \] Kombinieren wir die \(l\)-Terme: \[ \square = (141 - 27.8) l + 88.75 d l = 113.2 l + 88.75 d l \] Somit haben wir eine Lösung für \(\square\): \[ \square = 113.2 l + 88.75 d l \] Das ist die gesuchte Form, wobei das Resultat in Litern angegeben ist!

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