Question

Find the value of x in each of the following proportions:

(1) 8 : 12 = 2 : x
(2) 4 : 5 = x : 50
(3) x : 6 = 10 : 15
(4) 5 : x = 20 : 24

Answer 1

(1)
$$\begin{gathered} 8:12=2:x \\ =\frac{8}{12}=\frac{2}{x} \\ =\frac{8÷4}{12÷4}=\frac{2}{x} \\ =\frac{2}{3}=\frac{2}{x} \\ =x=3 \end{gathered}$$

(2)
$$\begin{gathered} 4:5=x:50 \\ =\frac{4}{5}=\frac{x}{50} \\ =4\times 50=5\times x \\ =200=5x \\ =x=\frac{200}{5} \\ =x=\frac{200÷5}{5÷5} \\ =x=\frac{40}{1} \\ =x=40 \end{gathered}$$

(3)
$$\begin{gathered} x:6=10:15 \\ =\frac{x}{6}=\frac{10}{15} \\ =x\times 15=6\times 10 \\ =15x=60 \\ =x=\frac{60}{15} \\ =x=\frac{60÷15}{15÷15} \\ =x=\frac{4}{1} \\ =x=4 \end{gathered}$$

(4)
$$\begin{gathered} 5:x=20:24 \\ =\frac{5}{x}=\frac{20}{24} \\ =x\times 20=5\times 24 \\ =20x=120 \\ =x=\frac{120}{20} \\ =x=\frac{6}{1} \\ =x=6 \end{gathered}$$