Question

A PE 4 = CU B PE 6 = CU C PE 8 SI 1 PE A +1 PE B +1 PE C =13 PE 144  URGENT 

Answer 1

Si trebuie sa afli a, b si c?

Answer 2

$\frac{a}{4} = \frac{b}{6} = \frac{c}{8}$

$\frac{1}{24} + \frac{1}{36} + \frac{1}{48}=\frac{13}{144}$

$\frac{a}{4} = \frac{b}{6}$⇒$6a =4b$⇒$a= \frac{4}{6} b= \frac{2}{3} b$

$\frac{b}{6} = \frac{c}{8}$⇒$6c =8b$⇒$c= \frac{8}{6} b= \frac{4}{3} b$

$\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{13}{144}$

⇒$\frac{1}{ \frac{2}{3}b } + \frac{1}{b} + \frac{1}{ \frac{4}{3} b} = \frac{13}{144}$

⇒$\frac{3}{ 2b} } + \frac{1}{b} + \frac{3}{4b} = \frac{13}{144}$

⇒$\frac{3*2+4+3}{ 4b} = \frac{13}{144}$⇒$\frac{13}{ 4b} = \frac{13}{144}$

⇒$13*144=13*4*b$⇒$b= \frac{13*144}{13*4} = \frac{144}{4} =36$

$a= \frac{2}{3} b= \frac{2}{3} *36=2*12=24$

$c= \frac{8}{6} b= \frac{4}{3} b=36* \frac{4}{3} =12*4=48$

Verificare:
$\frac{1}{24} + \frac{1}{36} + \frac{1}{48} = \frac{6+4+3}{144} =\frac{13}{144}$