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Lerok [7]
3 years ago
15

10x+4y+ 12z=120 11x +77y =220 8x +2y +32z =160

Mathematics
1 answer:
Damm [24]3 years ago
6 0

Answer:

x=8.94 ; y = 1.58; z=2.02

Step-by-step explanation:

solve 10x+4y+12z = 120      →          5x+2y+6z = 60

         8x + 2y +32Z = 160   →           4x+y+16z = 80

To eliminate z multiply first equation by 16 and second equation by 6.

80x+32y+96z = 960

24x+6y+96z =   480

on subtractionwe get 56x+26y = 480

dividing by 2 we get, 28x + 13y = 240

Now we have a given equation 11x + 77y = 220 → x + 7y = 20

solving 28x + 13y = 240 and x + 7y = 20

28x + 13y =240

28x + 216y = 560

subtracting we get, 203y = 320

y = 1.58

x = 8.94

z = 2.02

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Un padre cede al mayor de sus hijos la quinta parte de su capital, al segundo la cuarta parte del mismo y al tercero le da el re
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Answer:

El padre tenía un capital de 60,000 euros.

El hijo mayor recibe 12,000 euros.

El hijo segundo recibe 15,000 euros.

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Step-by-step explanation:

Sea x el capital total del padre y a,b,c son las asignaciones a los hijos mayor, segundo y tercero. A continuación, construimos las ecuaciones matemáticas a partir de lo descrito en el enunciado:

Hijo mayor

a = \frac{1}{5}\cdot x (1)

Hijo segundo

b = \frac{1}{4}\cdot x (2)

Hijo tercero

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De (3) tenemos que el capital del padre es:

x = \frac{33000}{1-\frac{1}{5}-\frac{1}{4}  }

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El padre tenía un capital de 60,000 euros.

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