Question

stiind ca a/b=b/m=c/p=1/5m,n,p calculati raportul a+b+c/n+m+p

Answer 1

Răspuns:1/5

Explicație pas cu pas:

OK cred ca la a doua trebuia sa scrii n/m pt ca altfel nu i vad rostul

Aplicam proprietatea proportilor⇒a*m=b*n=1/5; b*c=a*p= 1/5; m*c=n*p=1/5

⇒ca toate sunt egale deci: a+b+c/n+m+p=1/5

Sper ca te am ajutat

Answer 2

Cerinta:

"Stiind ca a/n = b/m = c/p = 1/5 calculati raportul (a + b + c) / (n + m + p)"

$\bf \dfrac{a}{n} = \dfrac{b}{m} =\dfrac{c}{p} = \dfrac{1}{5}$

folosind regula produsul mezilor este egal cu produsul extremilor vom scrie pe n,m,p in functie de a,b,c

$\bf\dfrac{a}{n}= \dfrac{1}{5}\Rightarrow 1\cdot n=5\cdot a\Rightarrow\boxed{\bf n=5a}$

$\bf\dfrac{b}{m}= \dfrac{1}{5}\Rightarrow 1\cdot m=5\cdot b\Rightarrow\boxed{\bf m=5b}$

$\bf \dfrac{c}{p} = \dfrac{1}{5} \Rightarrow 1\cdot p = 5\cdot c \Rightarrow\boxed{\bf p = 5c}$

Inlocuim si calculam:

$\bf\dfrac{a + b + c}{n + m +p}= \dfrac{a +b +c}{5a + 5b + 5c }\Rightarrow\\\\\\\dfrac{a + b + c}{n + m +p} = \dfrac{a +b +c}{5\cdot(a + b + c)}\Rightarrow\\\\\\\dfrac{a + b + c}{n + m +p} = \boxed{\bf\dfrac{1}{5} }$

Raspuns: a+b+c/n+m+p = 1/5