Question

RESUELVO LOS SIGUIENTES PLANTEAMENTOS :

A.repartir $1858 en partes directamente proporcionales a las edades 4, 7 y 12

B.repartir 950 en partes inversamente proporcionales a 3, 6 y 9

Answer 1

Al resolver los planteamientos se obtiene:

A. x = $323.15

   y = $565.47

   z = $969.39

B. x = $518.15

   y = $259.07

   z = $172.71

Explicación paso a paso:

A. reparto directamente proporcional;

$1858

Aplicar proporción directa;

$\frac{x}{a} =\frac{y}{b} =\frac{z}{c} = \frac{x+y+z}{a+b+c}$

Siendo;

x+y+z = 1858

a+b+c = 4+7+12 = 23

Sustituir;

$\frac{x}{4} =\frac{y}{7} =\frac{z}{12} = \frac{1858}{23}$

Calcular x;

$\frac{x}{4}=\frac{1858}{23}$

x = 4(1858/23)

x = $323.15

Calcular y;

$\frac{y}{7}=\frac{1858}{23}$

y = 7(1858/23)

y = $565.47

Calcular x;

$\frac{z}{12}=\frac{1858}{23}$

z = 12(1858/23)

z = $969.39

B. reparto inversamente proporcional;

Aplicar proporción inversa;

$\frac{a}{3} +\frac{a}{6} +\frac{a}{9} =950$

MCM = 18

$\frac{6a+3a+2a}{18} =950$

$\frac{11a}{18} =950$

11a = 18(950)

a = 17100/11

a = $1554.54

Sustituir;

x = 1554.45/3

x = $518.15

y = 1554.45/6

y = $259.07

z = 1554.45/9

z = $172.71