Alegria va a la tienda a comprar arroz y azucar, pero solo tine 20, si cada libra de arroz cuesta 0.60 y de azucar cuesta 0.80, cuantas libras de cada una le alcanzan para comprar

Answer:

Alegría puede comprar 16.667 libras de arroz y 12.5 libras de azúcar con 20 pesos.

Step-by-step explanation:

Sabemos que una libra de arroz cuesta 0.60 pesos, mientras que una de azúcar cuesta 0.80 pesos. Un enfoque posible es determinar cuantas libras de arroz se obtiene por el mismo dinero para adquirir una libra de azúcar a través de una regla de tres simple:

[tex]x = \frac{0.80\,\$}{0.60\,\$}\times 1\,lb[/tex]

[tex]x = \frac{4}{3}\,lb[/tex]

Esto quiere decir que por cada tres libras de azúcar, se compra cuatro libras de arroz. Ahora, la cantidad de alimentos que puede comprar Alegría queda restringida al dinero disponible (20 pesos) y se describe por la siguiente ecuación:

[tex]0.60\cdot x +0.80\cdot y = 20[/tex] (Ec. 1)

Donde:

[tex]x[/tex] - Cantidad de arroz, medida en libras.

[tex]y[/tex] - Cantidad de azúcar, medida en libras.

Además, la siguiente ecuación se deriva de la regla de tres del inicio del problema:

[tex]x = \frac{4}{3} \cdot y[/tex] (Ec. 2)

Si aplicamos (Ec. 2) en (Ec. 1) y resolvemos la ecuación resultante, tenemos que:

[tex]0.60\cdot \left(\frac{4}{3}\cdot y \right) + 0.80\cdot y = 20[/tex]

[tex]1.60\cdot y = 20[/tex]

[tex]y = 12.5\,lb[/tex]

De (Ec. 2) tenemos que la cantidad de arroz es:

[tex]x = 16.667\,lb[/tex]

En consecuencia, Alegría puede comprar 16.667 libras de arroz y 12.5 libras de azúcar con 20 pesos.

Alegría puede comprar 33.333 libras de arroz o 25 libras de azúcar.

Dado que Alegría va a la tienda a comprar arroz y azúcar, pero solo tiene $20, si cada libra de arroz cuesta $0.60 y de azúcar cuesta $0.80, para determinar cuántas libras de cada una le alcanzan para comprar se debe realizar el siguiente cálculo:

Por lo tanto, Alegría puede comprar 33.333 libras de arroz o 25 libras de azúcar.

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