Question

calculati nr rationale a,b,c stiind ca a/2=b/4=c/7 si 2a+b+5c=43

Answer 1

$\frac{a}{2} = \frac{b}{4} = \frac{c}{7} = k \Rightarrow a=2k, \ b=4k, \ c=7k \\ \\2a+b+5c=43 \Rightarrow 2*2k+4k+7*5k=43 \Rightarrow 43k=43 \Rightarrow k= 1 \Rightarrow a=2*1=2 ; \ b= 4*1 = 4 ; \ c= 7*1 = 7$

Answer 2

$\dfrac{a}{2} = \dfrac{b}{4} = \dfrac{c}{7} \Big|\cdot 4 \Rightarrow 2a = b = \dfrac{4c}{7} \\ \\ 2a+b+5c = 43 \Rightarrow \dfrac{4c}{7}+\dfrac{4c}{7}+5c = 43\Big|7 \Rightarrow 4c+4c+35c = 301 \Rightarrow \\ \\ \Rightarrow 43c = 301 \Rightarrow c = \dfrac{301}{43} \Rightarrow \boxed{c = 7} \\ \\ b = \dfrac{4\cdot 7}{7} \Rightarrow \boxed{b=4} \\ \\ 2a = \dfrac{4\cdot 7}{7} \Rightarrow 2a = 4 \Rightarrow \boxed{a = 2 }$