Question

If $5a+3b:3a+5b=3:4$, find $a:b$.

Answer 1

Calculation of the ratio $a:b$

The given ratio can be written as $\frac{5a+3b}{3a+5b}=\frac{3}{4}$.

$$\begin{gathered} \Rightarrow 4(5a+3b)=3(3a+5b)(Crossmultiplyingbothsides) \\ \Rightarrow 20a+12b=9a+15b \\ \Rightarrow 20a-9a=15b-12b(Separatingthevariablesaandbontobothsides) \\ \Rightarrow 11a=3b \\ \Rightarrow \frac{11a}{b}=\frac{3}{1}(Divingbothsidesbyb,b\ne 0) \\ \Rightarrow \frac{a}{b}=\frac{3}{11}(Divingbothsidesby11) \\ \therefore a:b=3:11 \end{gathered}$$

Final Answer: The ratio for $a:b$ is $3:11$.