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2.2. ¡De gira con tu grupo!

¡De gira con tu grupo!

De gira

Grupo musical ensayando en el campo

¿Quién no ha soñado con hacer una gira con su grupo de rock favorito?

Si es tu caso, vas a ayudar a preparar el viaje.

Imagina que tienes que contabilizar los gastos. Sabes que, con el presupuesto actual, es suficiente para 3 personas durante 10 días.

En el último momento se incorporan dos personas más. ¿Para cuántos días llegaría el mismo presupuesto?

Reparte

Está claro que se trata de un problema de proporcionalidad, de reparto.

¿Recuerdas los pasos para resolverlo?

  1. Identificar las magnitudes que intervienen.
  2. Ordenarlas con sus datos y su incógnita.
  3. Identificar el tipo de proporcionalidad.

¿Directa o inversa?

Cuando comparas dos magnitudes, debes comprobar si la primera cambia de forma multiplicativa con la segunda.

En el caso de que al multiplicar la primera por un número la segunda también quede multiplicada por ese número, ambas son directamente proporcionales.

También puede ocurrir que la segunda quede dividida por ese número, en ese caso serían inversamente proporcionales.

Si no ocurre ninguna de las dos cosas, no guardan relación proporcional (ni directa, ni inversa).

Intenta resolver el problema y, si no sabes, consulta la ayuda.

¡Si sois más, os toca a menos!

Analiza...

  • Identifica las magnitudes: número de personas y tiempo que dura el presupuesto.
  • Ordena los datos y localiza la incógnita x = tiempo que dura el presupuesto.
  • Identifica el tipo de proporcionalidad: si aumenta el número de personas, el presupuesto dura menos tiempo; es inversa.

Organiza

Escribe los datos en forma de tabla, poniendo en el encabezado las magnitudes.

Puede ayudarte indicar con una flecha la relación entre ellas.

↑ personas tiempo ↓
 3 personas → 10 días
5 personas → x días

Resuelve

Al ser una relación inversa, una de las razones es proporcional a la inversa de la otra.

A 3/5 se le hace la razón inversa; 5/3.

\( \dfrac{5}{3} = \dfrac{10}{x} \) ⇒ x = 6 días

Reparto del gasto inicial del grupo

Para planear la próxima gira del grupo, ponéis un fondo común que de 600 €.

Completa la tabla con la cantidad de dinero que debe poner cada persona, en cada caso.

N.º de miembros del grupo Dinero que pone cada uno
3
4
5
6

La constante de proporcionalidad es el dinero que hay que repartir: €.

¿Qué tipo de relación existe entre las magnitudes integrantes y participación? .

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El precio de las entradas

Lee el texto y completa las palabras que faltan.

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Si 5 entradas cuestan 75 €, ¿cuánto cuestan 400 entradas?

↑ entradas Entradas ↑
@@5@@ entradas → @@75@@ €
@@400@@ entradas → @@x@@  €

El resultado es: x = @@6000@@ €

Si prefieres hacerlo por reducción a la unidad, calcula primero cuánto cuesta una entrada: @@15@@ €

Su navegador no es compatible con esta herramienta.

Después del último acorde

Lee el texto y completa las palabras que faltan.

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Tras la última canción, hay que dejar el local impecable.

Si contratas a 3 personas, tardan 8 horas en recoger todo el material.

La organización dice que solo tenéis 2 horas antes de que se cierre el recinto.

¿Cuántos personas necesitáis?

↑ personas horas ↓
 3 personas → 8 horas 
x personas → 2 horas

El resultado es: x = @@12@@ personas

Su navegador no es compatible con esta herramienta.

Feito con eXeLearning (Nova xanela)