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ZanzabumX [31]
3 years ago
11

13. En un pueblo, 5 personas escucharon una noticia. En una hora, cada una de ellas

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
7 0

Answer:

En 5 horas se habrá enterado todo el pueblo.

Step-by-step explanation:

Sabemos que en un pueblo 5 personas escucharon una noticia.

Una hora más tarde, cada una de ellas le contó la noticia a otras 5.

Luego, éstas contaron la noticia a otras 5 y así sucesivamente.

Nadie cuenta ni escucha la noticia más de una vez y en ese pueblo hay un poco más de 19000 habitantes.

La ecuación a desarrollar para resolver el problema es la siguiente :

Comenzamos con 5 personas que escucharon la noticia a la ''hora 0''.

Una hora más tarde, cada una de ellas le contó a 5 personas, es decir , pasada la primera hora tendremos :

5+5^{2}=30 (I)

Las 5 personas originales de la ''hora 0'' más 25 personas que se enteraron pasada la primera hora. La ecuación que planteamos es la siguiente :

5^{1}+5^{2}+5^{3}+...+5^{x}>19000 (II)

Buscamos el valor de x que satisface la ecuación (II).

Probando y realizando las sumas encontramos que :

5^{1}+5^{2}+5^{3}+5^{4}+5^{5}+5^{6}>19000

19530>19000

El valor de x que satisface (II) es x=6.

Para hallar el número de horas nos fijamos que en (I) el valor del mayor exponente del 5 es el número 2. Para ese valor 2, el tiempo que pasó es una hora.

Entonces para nuestro x=6, el número de horas que pasaron son 5 horas (1 menos que el valor de x)

Todo el pueblo se habrá enterado en 5 horas de la noticia.

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When Rafael emptied his pockets, e found he had a total of $3.50 in quarters and nickels. If he had 8 more quarters that nickels
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You can use systems of equations for this one.

We are going to use 'q' as the number of quarters Rafael had,
and 'n' as the number of nickels Rafael had.


You can write the first equation like this:
3.50=0.05n+0.25q
This says that however many 5 cent nickels he had, and however many
25 cent quarters he had, all added up to value $3.50.
Our second equation is this:
q=n+8
This says that Rafael had 8 more nickels that he had quarters.

We can now use substitution to solve our system.

We can rewrite our first equation from:
3.50=0.05n+0.25q
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3.50=0.05n+0.25(n+8)

From here, simply solve using PEMDAS.

3.50=0.05n+0.25(n+8)     --Distribute 0.25 to the n and the 8
3.50=0.05n+0.25n+2     --Subtract 2 from both sides
1.50=0.05n+0.25n     --Combine like terms
1.50=0.30n     --Divide both sides by 0.30
5=n     --This is how many NICKELS Rafael has.

We now know how many nickels he has, but the question is asking us
how many quarters he has.

Simply substitute our now-known value of n into either of our previous
equations (3.50=0.05n+0.25q or q=n+8) and solve.

We now know that Rafael had 13 quarters.

To check, just substitute our known values for our variables and solve.
If both sides of our equations are equal, then you know that you have
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Happy math-ing :)
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