Question

Determinati numerele naturale x si y,astfel incat:​

Answer 1

Răspuns:

Explicație pas cu pas:

a) x+y=98

5x=2y

 x=2/5y

(2/5 )*y+y=98

7*y=98*5

y=70

x=28

b) y-x=24

7x=3y

rezulta: x=(3/7)* y

y- (3/7) * y=24

4y=24*7

y=42

x=3/7*(42)=18

Answer 2

$\it a)\ \ x+y=98\ \ \ \ \ (*)\\ \\ \\ \dfrac{x}{y}=\dfrac{2}{5} \Rightarrow \dfrac{x}{2}=\dfrac{y}{5} =\dfrac{x+y}{2+5}\ \stackrel{(*)}{=}\dfrac{98}{7}=14\Rightarrow\begin{cases} \it \dfrac{x}{2}=14 \Rightarrow x=2\cdot14=28\\ \\ \it \dfrac{y}{5}=14 \Rightarrow y=5\cdot14=70\end{cases}$

b)

$\it y-x=24\ \ \ \ \ (*)\\ \\ \\ \dfrac{y}{x}=\dfrac{7}{3} \Rightarrow \dfrac{y}{7}=\dfrac{x}{3}=\dfrac{y-x}{7-3}\ \stackrel{(*)}{=}\ \dfrac{24}{4}=6 \Rightarrow\begin{cases} \it \dfrac{x}{3}=6 \Rightarrow x=3\cdot6=18\\ \\ \\\it \dfrac{y}{7}=6 \Rightarrow y=7\cdot6=42\end{cases}$