Question

If (3a+2b) : (5a+3b) = 18 : 29, find a : b

• A. 3:2
• B. 4:3
• C. 1:1
• D. 5:3

Answer 1

The correct option is B

4:3

$\frac{3a+2b}{5a+3b}=\frac{18}{29}\Rightarrow \frac{b[3\left(\frac{a}{b}\right)+2]}{b[5\left(\frac{a}{b}\right)+3]}=\frac{18}{29}$
Let $\frac{a}{b}=x$
Then, $29(3x+2)=18(5x+3)\Rightarrow 87x+58=90x+54\Rightarrow 87x-90x=-58+54\Rightarrow -3x=-4\Rightarrow x=\frac{4}{3}\therefore \frac{a}{b}=\frac{4}{3}\Rightarrow a:b=4:3$