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denpristay [2]
3 years ago
10

Mezclas de alimentos. Un chef repostero creó una solución de azúcar de 50 onzas constituida por 34% de azúcar con una solución d

e azúcar al 20% y otra solución al 40%. ¿Qué cantidad utilizó de la solución de azúcar al 20% y de la solución al 40%?
Mathematics
1 answer:
Kay [80]3 years ago
4 0

Answer:

Las cantidades empleadas para su preparación son: 15 onzas de solución al 20 % y 35 onzas de solución al 40 %.

Step-by-step explanation:

Podemos estimar la proporción de ingredientes mediante el siguiente promedio ponderado:

0.34= \frac{0.2\cdot m_{A} + 0.4\cdot m_{B}}{m_{A}+m_{B}} (1)

Donde:

m_{A} - Masa de la solución al 20 %, en onzas.

m_{B} - Masa de la solución al 40 %, en onzas.

Podemos simplificar la formula como sigue:

0.2\cdot x + 0.4\cdot (1-x) = 0.34 (2)

Donde x es la proporción de la solución al 20 % dentro de la solución final, sin unidades.

Ahora resolvemos para x en (2):

0.4-0.2\cdot x = 0.34

0.2\cdot x = 0.06

x = \frac{0.06}{0.2}

x = 0.3

Este resultado quiere decir que la solución al 34 % es el resultado de 30 % de la solución al 20 % y 70 % de la solución al 40 %. Si conocemos que la solución final tiene una masa de 50 onzas, entonces las cantidades empleadas para su preparación son: 15 onzas de solución al 20 % y 35 onzas de solución al 40 %.

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