Question

Suma a doua nr este 210. Raportul nr este trei pe patru. Care sunt cele doua nr?

Answer 1

Fie a si b numerele.

$a+b=210 \\ \\ \frac{a}{b}= \frac{3}{4}=>4a=3b \\ \\ a+b=210<=>3a+3b=630<=>3a+4a=630<=> 7a=630 \\ =>a=90. \\ \\ b=210-a=210-90=120.$

Answer 2

[tex]a+b=210\\ \frac{a}{b}= \frac{3}{4}\overset{P.F.P.}{\Longrightarrow} 4a=3b(1)\\ a+b=210\Rightarrow 3a+3b=630(2)\\ \text{Inlocuim~(2)~in~(1):}\\ 3a+4a=630\Leftrightarrow 7a=630\Rightarrow \boxed{a=90}\Rightarrow \boxed{b=120.}\\\\ P.F.P.-\text{Proprietatea~fundamentala~a~proportiilor}[/tex]