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Umnica [9.8K]
3 years ago
10

El administrador de una cafetería sabe que vende diariamente 50 litros de jugo mixto. Para elaborar este jugo se emplean dos pre

parados: uno de jugo de naranja, que contiene un 5% de jugo natural y otro preparado de jugo de toronja, que contiene 25% de jugo natural. Si se desea que el jugo mixto contenga un 10% de jugo natural ¿Cuántos litros de cada preparado se deben emplear?
Mathematics
1 answer:
Nina [5.8K]3 years ago
7 0

Answer:

Se necesitan 37.5 litros del preparado que contiene 5% de jugo natural, y 12.5 litros del que contiene 25%.

Step-by-step explanation:

Primero calculamos la cantidad total de jugo natural que se necesita, a partir del volumen de jugo mixto que se quiere vender:

  • 50 L * 10/100 = 5 L

Ahora, que X sean los litros del preparado con jugo de 5%, y que Y sean los litros del preparado con jugo de 25%:

La suma de ambos preparados tiene que ser 50 L:

1.    x + y = 50

La suma del jugo natural tiene que ser 5:

2.   x*5/100 + y*25/100 = 5

Por lo que tenemos <em>un sistema de dos ecuaciones y dos incognitas</em>.

Expresamos x en términos de y:

  • x + y = 50
  • x = 50 - y

Reemplazamos x en la segunda ecuación:

  • (50-y)*5/100 + y*25/100 = 5

Y despejamos <em>y</em>:

  • 2.5 - 0.05y + 0.25y = 5
  • 0.20y = 2.5
  • y = 12.5

Usando ese valor de y, calculamos x:

  • x + 12.5 = 50
  • x = 37.5

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