Question

Află numerele x y z știind că sunt invers proporționale cu 4, 10, 5 și că x+3z=34
Va rog ajutatima

Answer 1

 

$\displaystyle\\x;~y;~z~~\text{sunt invers proportionale cu}~~4;~10;~5\\\\4x=10y=5z=k\\\\x=\frac{k}{4}\\\\y=\frac{k}{10}\\\\z=\frac{k}{5}\\\\x+3z=34\\\\\frac{k}{4}+3\cdot\frac{k}{5}=34\\\\\frac{k\cdot5}{4\cdot5}+\frac{3\cdot k\cdot4}{5\cdot4}=34\\\\\frac{5k}{20}+\frac{12k}{20}=34\\\\\frac{5k+12k}{20}=34\\\\\frac{17k}{20}=34\\\\17k=34\cdot20\\\\k=\frac{34\cdot20}{17}\\\\k=2\cdot20\\\\\boxed{k=40}$

$\displaystyle\\\\x=\frac{k}{4}=\frac{40}{4}=\boxed{10}\\\\y=\frac{k}{10}=\frac{40}{10}=\boxed{4}\\\\z=\frac{k}{5}=\frac{40}{5}=\boxed{8}$

Answer 2

Răspuns

Explicație pas cu pas:

[ x;  y;  z ]    i. p.  [ 4;   10;  5 ]  

x / ( 1 / 4 ) = y / ( 1 / 10 ) = z / ( 1 / 5 ) = k

x / ( 1 / 4 ) = x :  1 / 4 = x ·  4 / 1 = 4 x

⇒   4 x = 10 y = 5 z = k ⇒   x = k / 4;    y = k / 10   si  z = k / 5

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x + 3 z = 34

k / 4 + 3 × k / 5 = 34

→ c.m.m.m.c al numitorilor 4 si 5 este 20

= 5 k + 4 × 3 k = 20 × 34

5 k + 12 k = 680  

17 k = 680

k = 680 : 17    ⇒   k = 40

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x = k / 4  ⇒  x = 40 / 4    ⇒    x = 10

y = k / 10 ⇒  y = 40 / 10  ⇒    y = 4

z = k / 5  ⇒   z = 40 / 5    ⇒     z = 8