Question

Determinati fractia a/b stiind ca este egala cu fractia 2/3 si ca a+b=10

Answer 1

$\displaystyle \bold{Raspuns:} \ \frac{a}{b}=\frac{4}{6} \\\\\\{\textbf{Explicatie pas cu pas:}}} \\\\ \textbf{(1) Notam:}\\\\ \frac{a}{b}=\frac{2}{3} \\ \\ a+b=10 \\ \\ \textbf{(2) Scoatem pe a din prima relatie si inlocuim:}\\ \frac{a}{b}=\frac{2}{3} \to \boxed{a=\frac{2 \cdot b}{3} }\\\\ \frac{2b}{3} +b=10 \\ \\ \bullet \text{aducem la aceelasi numitor ca sa scapam de fractii}\\ \frac{2b}{3} +\raisebox{\baselineskip}{3)}b=\raisebox{\baselineskip}{3)}10\\ \\ 2b+3b=30\\ 5b=30\\ b=30:5\\ \boxed{b=6}$

$\displaystyle \textbf{(3) Inlocuim pe b si aflam cat e a}\\ a+6=10\\ a=10-6\\ \boxed{a=4}$