Question

if a-b:a+b=1:11,find the ratio between 5a+4b+15:5a+4b-3.

Answer 1

Given that
$\frac{a-b}{a+b}=\frac{1}{11}$

To find: $\frac{5a+4b+15}{5a+4b-3}$

$$\begin{gathered} \frac{a-b}{a+b}=\frac{1}{11} \\ u\sin gCrossmultiplication \\ \Rightarrow 11(a-b)=1(a+b) \\ \Rightarrow 11a-11b=a+b \\ \Rightarrow 10a=12b \\ \Rightarrow 5a=6b \\ \Rightarrow b=\frac{5}{6}a \end{gathered}$$

$$\begin{gathered} onplugging5a=6b \\ \frac{5a+4b+15}{5a+4b-3}=\frac{6b+4b+15}{6b+4b-3}=\frac{10b+15}{10b-3} \end{gathered}$$

$$\begin{gathered} onpluggingb=\frac{5}{6}a \\ \frac{5a+4b+15}{5a+4b-3}=\frac{5a+4\left({\displaystyle \frac{5}{6}}\right)a+15}{5a+4\left({\displaystyle \frac{5}{6}}\right)a-3} \\ onmultiplying6withnumeratoranddenominator \\ =\frac{30a+20a+90}{30a+20a-18}=\frac{50a+90}{50a-18} \\ ondividingby2innumeratoranddenominator \\ =\frac{25a+45}{25a-9} \end{gathered}$$
final answer would be in terms of b or a.