Question

Va rog mult!Dau coroana.​

Answer 1

Explicație pas cu pas:

a)

$\frac{a}{2} = \frac{b}{11} = \frac{c}{7} = \frac{a + b + c}{2 + 11 + 7} = \frac{80}{20} = 4 \\ \frac{a}{2} = 4 \implies \bf a = 8 \\ \frac{b}{11} = 4 \implies \bf b = 44 \\ \frac{c}{7} = 4 \implies \bf c = 28$

b)

$\frac{a}{5} = \frac{b}{3} = \frac{c}{7} = k \\ a = 5k; \ \ b = 3k; \ \ c = 7k$

$a + 2b - c = 192$

$5k + 2 \cdot 3k - 7k = 192 \\ 4k = 192 \implies k = 48$

$a = 5 \cdot 48 \implies \bf a = 240 \\ b = 3 \cdot 48 \implies \bf b = 144 \\ c = 7 \cdot 48 \implies \bf c = 336$

Answer 2

$\it a+2b-c=192\ \ \ \ \ (*)\\ \\ \\ \dfrac{a}{5}=\dfrac{^{2)}b}{\ \ 3}=\dfrac{c}{7} \Rightarrow \dfrac{a}{5}=\dfrac{2b}{6}=\dfrac{c}{7}=\dfrac{a+2b-c}{5+6-7}\ \stackrel{(*)}{=}\ \dfrac{192}{4}=48\ \Rightarrow\\ \\ \\ \Rightarrow\ \begin{cases} \it \dfrac{a}{5}=48 \Rightarrow a=5\cdot48 =240\\ \\ \\ \it \dfrac{2b}{6}=48 \Rightarrow 2b=6\cdot48=288 \Rightarrow b=288:2=144\\ \\ \\ \it \dfrac{c}{7}=48 \Rightarrow c=7\cdot48=336\end{cases}$