Question

Divida o número 252 em partes diretamente proporcionais a 3, 4 e 5

Answer 1

21.3=63
21.4=84
21.5=105

CALCULO:
12x=252
x=252
     12
x=21 

Answer 2

$a+b+c=252$

$\dfrac{a}{3}=\dfrac{b}{4}=\dfrac{c}{5}$

$\dfrac{a}{3}=\dfrac{b}{4} \iff 3b=4a \iff b=\dfrac{4a}{3}$

$\dfrac{a}{3}=\dfrac{c}{5} \iff 3c=5a \iff c=\dfrac{5a}{3}$

Substituindo na primeira equação:

$a+\dfrac{4a}{3}+\dfrac{5a}{3}=252$

$3a+4a+5a=756$

$12a=756 \iff a=\dfrac{756}{12} \iff \boxed{a=63}$

Assim:

$b=\dfrac{4a}{3} \iff b=\dfrac{4\cdot63}{3} \iff b=\dfrac{252}{3} \iff \boxed{b=84}$

$c=\dfrac{5a}{3} \iff c=\dfrac{5\cdot63}{3} \iff c=\dfrac{315}{3} \iff \boxed{c=105}$