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3 years ago

12

Vicente se gasta 20 euros en un pantalón y una camisa. No sabe el precio de cada prenda, pero sí sabe que la camisa vale dos qui

ntas partes de lo que vale el pantalón. ¿Cuánto vale el pantalón?

1 answer:

Vlad1618 [11]3 years ago

8 0

Answer:

14.3€

Step-by-step explanation:

Let:

$C=Price\hspace{3}of\hspace{3}the\hspace{3}shirt\\P=Price\hspace{3}of\hspace{3}the\hspace{3}pants\\T=Total\hspace{3}cost$

Now, let's write the data provided by the problem, using algebraic notation.

The total cost of the clothes is 20€, so:

$P+C=T\\\\P+C=20$

The price of the shirt is :

$C=\frac{2}{5} P$

Replacing this value into the first equation:

$P+\frac{2}{5} P=20$

Solving for P:

$\frac{7}{5} P=20\\\\P=\frac{100}{7} \approx 14.3$

So, the price of the pants is 14.3€ and the price of the shirt is:

$C+14.3=20\\\\C=20-14.3=5.7$

Translation:

Deja que:

$C=Precio\hspace{3}de\hspace{3}la\hspace{3}camisa\\P=Precio\hspace{3}del\hspace{3}pantalon\\T=Costo\hspace{3}total$

Ahora, escribamos los datos proporcionados por el problema, usando notación algebraica.

El costo total de la ropa es de 20 €, entonces:

$P+C=T\\\\P+C=20$

El precio de la camisa es:

$C=\frac{2}{5} P$

Reemplazando este valor en la primera ecuación:

$P+\frac{2}{5} P=20$

Resolviendo para P:

$\frac{7}{5} P=20\\\\P=\frac{100}{7} \approx 14.3$

Entonces, el precio del pantalón es de 14.3 € y el precio de la camisa es:

$C+14.3=20\\\\C=20-14.3=5.7$

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