Question

Find x in the following proportions:

(i) x : 6 = 55 : 11
(ii) 18 : x = 27 : 3
(iii) 7 : 14 = 15 : x
(iv) 16 : 18 = x : 96

Answer 1

(i) x : 6 = 55 : 11
$$\begin{gathered} \Rightarrow \frac{x}{6}=\frac{55}{11} \\ \Rightarrow \frac{x}{6}=\frac{5}{1} \\ \Rightarrow x=5\times 6=30 \end{gathered}$$

(ii) 18 : x = 27 : 3

$$\begin{gathered} \Rightarrow \frac{18}{x}=\frac{27}{3} \\ \Rightarrow \frac{18}{x}=\frac{9}{1} \\ \Rightarrow x=\frac{18}{9}=2 \end{gathered}$$
(iii) 7 : 14 = 15 : x

$$\begin{gathered} \Rightarrow \frac{7}{14}=\frac{15}{x} \\ \Rightarrow \frac{1}{2}=\frac{15}{x} \\ \Rightarrow x=15\times 2=30 \end{gathered}$$

(iv) 16 : 18 = x : 96
$$\begin{gathered} \Rightarrow \frac{16}{18}=\frac{x}{96} \\ \Rightarrow \frac{8}{9}=\frac{x}{96} \\ \Rightarrow x=\frac{8}{9}\times 96=\frac{256}{3} \end{gathered}$$