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Lemur [1.5K]
3 years ago
12

Tres amigos: Andrés, Braulio y Ciro, juegan 3 apuestas

Mathematics
1 answer:
skelet666 [1.2K]3 years ago
7 0

Answer:

La persona que ganó más dinero fue Braulio por S/.16

Step-by-step explanation:

Deje que la cantidad inicial sea Andrés X, Braulio Y y Ciro Z

Luego, dado que cada uno pierde una apuesta en el orden presentado, tenemos;

Después de la primera apuesta, tenemos;

Andrés X-Y-Z, Braulio (Y + Y), Ciro (Z + Z)

En la segunda apuesta, tenemos;

2 (X-Y-Z), 2Y - (X-Y-Z) - 2Z, 2Z + 2Z

2 (X-Y-Z), 3Y - X -Z, 4Z

En el tercero

4 (X-Y-Z), 6Y - 2X - 2Z, 4Z-2 (X-Y-Z) - (3Y - X -Z)

4 (X-Y-Z), 6Y - 2X - 2Z, 7Z - X - Y

4 (X-Y-Z) = 0.48 .............................. (1)

6Y - 2X - 2Z = 0.56 ...................... (2)

7Z - X - Y = 0.28 ............................ (3)

Multiplicamos las ecuaciones (2) por 2 y restamos la ecuación (1), tenemos;

12Y - 4X - 4Z - 4X + 4Y + 4Z = 0.56 * 2 - 0.48 = 0.64

16Y - 8X = 0.64 ...................... (4)

Multiplicamos las ecuaciones (2) por 7/2 y sumamos a la ecuación (3), tenemos;

21Y - 7X - 7Z + 7Z - X - Y = 7/2 * 0.56 + 0.28

20Y - 8X = 2.24 ...................... (5)

Restando la ecuación (4) de la ecuación (5) tenemos;

20Y - 8X - 16Y - 8X = 2.24 - 0.64 =

4Y = 1.6

Y = 1.6 / 4 = 0.4

De la ecuación (5), tenemos;

20Y - 8X = 20 * 0.4 - 8X = 2.24

8X = 8 - 2.24 = 5.76

X = 5,76 / 8 = 0,72

De la ecuación (3), tenemos;

7Z - X - Y = 7Z - 0.72 - 0.4 = 0.28

7Z = 1.4

Z = 1.4 / 7 = 0.2

Por lo tanto tienen inicialmente

X₁ = 0.72

Y₁ = 0.4

Z₁ = 0.2

Después de jugar tienen;

X₂ = 0.48

Y₂ = 0.56

Z₂ = 0.28

Los cambios son

Andrés 0.48 - 0.72 = -0.24

Braulio; 0.56 - 0.4 = 0.16

Ciro 0.28 - 0.2 = 0.08

La persona que ganó más dinero fue Braulio por S/.16

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