Question

20. Se dă proporția: Aflați numerele x şi y ştiind că: a) x - y = 24; b) x + y = 36 c) 2x + 3y = 58.​

Answer 1

Răspuns:

a) x*5=y*7 x=1.4y 0.4y=24 y=24*2+(24:2)=60

x=60+24=84

b)x*5=y*7 x=1.4y

x+y=2.4y

2.4y= 36 y=36:2.4=15

y=15

x=15+(15*0.4) 15+6=21

x=21

c)2x+3y=58

x*5=y*7

x=1.4y

5.8y=58

y=58:5.8=10

y=10

x=1.4y

x=14

Answer 2

$\it a)\ \ x-y=24\\ \\ \\ \dfrac{x}{y}=\dfrac{7}{5} \Rightarrow \dfrac{x}{7}=\dfrac{y}{5}=\dfrac{x-y}{7-5}=\dfrac{24}{2}=12 \Rightarrow \begin{cases} \it x=7\cdot12=84\\ \\ \it y=5\cdot12=60 \end{cases}$

$\it b)\ \ x+y=36\\ \\ \\ \dfrac{x}{y}=\dfrac{7}{5} \Rightarrow \dfrac{x}{7}=\dfrac{y}{5}=\dfrac{x+y}{7+5}=\dfrac{36}{12}=3 \Rightarrow \begin{cases} \it x=7\cdot3=21\\ \\ \it y=5\cdot2=15 \end{cases}$

$\it c)\ \ 2x+3y=58\\ \\ \\ \dfrac{x}{y}=\dfrac{7}{5} \Rightarrow \dfrac{^{2)}x}{\ 7}=\dfrac{^{3)}y}{\ 5}\ \Rightarrow \dfrac{2x}{14}=\dfrac{3y}{15}=\dfrac{2x+3y}{14+15}=\dfrac{58}{29}=2 \Rightarrow \\ \\ \\ \Rightarrow \begin{cases} \it 2x=14\cdot2|_{:2} \Rightarrow x=14\\ \\ \it 3y=15\cdot2|_{:3} \Rightarrow y=10 \end{cases}$