Question

Fie $\frac{a}{b} = \frac{2}{7}$ Valoarea raportului$\frac{2a+3b}{5a+2b}$ este:

A) 23 pe 10
B) 27 pe 29
C) 25 pe 24
D)17 pe 19

Va rog cu explicatie.

Answer 1

$\it \dfrac{a}{b}=\dfrac{2}{7} \Rightarrow \dfrac{b}{a}=\dfrac{7}{2} \Rightarrow \dfrac{b}{a}=3,5 \Rightarrow b=3,5a\ \ \ \ \ (*)\\ \\ \\ \dfrac{2a+3b}{5a+2b}\ \stackrel{(*)}{=}\ \dfrac{2a+3\cdot3,5a}{5a+2\cdot3,5a}=\dfrac{a(2+10,5)}{a(5+7)}=\dfrac{^{2)}12,5}{12}=\dfrac{25}{24}$