Question

raportul a doua numere este 3/11 iar daca se mareste numaratorul cu 75 raportul devine 21/22. aflati cele doua numere

Answer 1

$\rm Fie ~a~si~ b~numerele~(b \neq 0). \\ \\ \frac{a}{b}= \frac{3}{11} \\ \\ \frac{a+75}{b}= \frac{21}{22} \Leftrightarrow \frac{a}{b}+ \frac{75}{b}= \frac{21}{22} \Leftrightarrow \frac{3}{11}+ \frac{75}{b}= \frac{21}{22} \Leftrightarrow \frac{75}{b} = \frac{21}{22}- \frac{3}{11} \Leftrightarrow \\ \\ \Leftrightarrow \frac{75}{b}= \frac{21-6}{22} \Leftrightarrow \frac{75}{b}= \frac{15}{22} \Rightarrow b= \frac{75 \cdot 22}{15}= 110.$

$\rm \frac{a}{b}= \frac{3}{11} \Rightarrow a= \frac{3b}{11}= \frac{3 \cdot 110}{11}=30. \\ \\ \underline{Solutie}: (a,b)=(30,110).$