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zavuch27 [327]
2 years ago
8

Camilo practica tiro al blanco. En cada disparo acertado puede obtener 5, 8, o 10 puntos. En su última práctica, su puntuación t

otal fue de 99, él obtuvo 8 puntos tantas veces como 10 puntos. Si en el 75% de las veces acertó al blanco, ¿cuántos disparos hizo Camilo en total?
Mathematics
1 answer:
Radda [10]2 years ago
8 0

Answer:

20 disparos

Step-by-step explanation:

Primera etapa es de determinar cuantos tiros de Camilo acertaron al blanco.

Sabemos que en su última práctica, obtuvo 99 puntos con una mezcla de 5, 8 y 10 puntos.  Eso puedo se exprimir así:

5x + 8y + 10x = 99

Sabemos también que el obtuvo tantos tiros de 8 puntos que de 10 puntos, entonces

y = z

Podemos mezclar las 2 ecuaciones y substituir y por z:

5x + 8y + 10y = 99

5x +18y = 99

Una ecuación, dos variables... no es fácil... pero son números pequeños y se puede intentar soluciones.  Entonces, cuantas veces podemos multiplicar 5 y 18 para obtener 99?

El más simple es de hacer la tabla de multiplicación de 18 y ver cual número nos deja con un multiple de 5.

18 x 1 = 18 (99 - 18 = 81, no un multiple e 5)

18 x 2 = 36 (99 - 36 = 63, no un multiple de 5)

18 x 3 = 54 (99 - 54 = 45, SI, un multiple de 5)

18 x 4 = 72 (99 - 72 = 27, no un multiple de 5)

18 x 5 = 90 (99 - 90 = 9, no un multiple de 5)

Entonces, sabemos que y = 3 y z = 3

5x + 18 (3) = 99

5x + 54 = 99

5x = 45

x = 9

El tiró 9 veces por 5 puntos, 3 veces por 8 puntos y 3 veces pour 10 puntos.

En total tiró 15 veces.

Si acertó 75% (3/4) de las veces, cuantos tiros total?

\frac{15}{3/4} = \frac{15 * 4}{3} = 20

Camilo tiró 20 veces en total.

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