Questions: La suma de dos números es 36. El número más pequeño es 6 menos que el número más grande. ¿Cuáles son los números? Número más grande: Número más pequeño:

La suma de dos números es 36. El número más pequeño es 6 menos que el número más grande. ¿Cuáles son los números? Número más grande: Número más pequeño:
Transcript text: La suma de dos números es 36. El número más pequeño es 6 menos que el número más grande. ¿Cuáles son los números? Número más grande: Número más pequeño:
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Solution

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Paso 1: Plantear las ecuaciones

Sea \( x \) el número más grande y \( y \) el número más pequeño. Según el problema, tenemos las siguientes ecuaciones:

  1. La suma de los dos números es 36: \[ x + y = 36 \]

  2. El número más pequeño es 6 menos que el número más grande: \[ y = x - 6 \]

Paso 2: Sustituir la segunda ecuación en la primera

Sustituimos la ecuación \( y = x - 6 \) en la ecuación \( x + y = 36 \):

\[ x + (x - 6) = 36 \]

Paso 3: Resolver la ecuación

Simplificamos y resolvemos la ecuación:

\[ 2x - 6 = 36 \]

Sumamos 6 a ambos lados:

\[ 2x = 42 \]

Dividimos entre 2:

\[ x = 21 \]

Paso 4: Encontrar el valor de \( y \)

Usamos el valor de \( x \) para encontrar \( y \):

\[ y = x - 6 = 21 - 6 = 15 \]

Respuesta Final

El número más grande es \(\boxed{21}\).

El número más pequeño es \(\boxed{15}\).

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