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500-506 Calcola \( x, y, z \) utilizzando i seguenti dati. \( x+y+z=110 \quad x: 2=y: 3=z: 6 \)

Ask by Nguyen Lawson. in Italy
Mar 15,2025

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\( x = 20 \), \( y = 30 \), \( z = 60 \).

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Per risolvere il sistema di equazioni, cominciamo con la relazione \( x:2 = y:3 = z:6 \). Possiamo esprimere \( x, y, z \) in termini di una variabile comune, diciamo \( k \): \[ x = 2k, \quad y = 3k, \quad z = 6k \] Ora sostituiamo queste espressioni nella prima equazione: \[ 2k + 3k + 6k = 110 \] Questo si semplifica a: \[ 11k = 110 \] Da cui troviamo \( k \): \[ k = \frac{110}{11} = 10 \] Ora possiamo calcolare \( x, y, z \): \[ x = 2k = 2 \cdot 10 = 20 \] \[ y = 3k = 3 \cdot 10 = 30 \] \[ z = 6k = 6 \cdot 10 = 60 \] Quindi, i valori sono \( x = 20 \), \( y = 30 \), e \( z = 60 \).

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