Question

If x and y are directly proportional, find the values of x₁ , x₂ and y₁ in the table given below:

x	3	x1	x2	10
y	72	120	192	y1

Answer 1

$$\begin{gathered} \mathrm{Since}x\mathrm{and}y\mathrm{are}\mathrm{directly}\mathrm{propotional},\mathrm{we}\mathrm{have}: \\ \frac{3}{72}=\frac{x_1}{120}=\frac{x_2}{192}=\frac{10}{y_1} \\ \mathrm{Now},\frac{3}{72}=\frac{x_1}{120} \\ \Rightarrow x_1=\frac{120\times 3}{72}=5 \end{gathered}$$

$$\begin{gathered} \mathrm{And},\frac{3}{72}=\frac{x_2}{192} \\ \Rightarrow x_2=\frac{3\times 192}{72}=8 \end{gathered}$$
$$\begin{gathered} \mathrm{And},\frac{3}{72}=\frac{10}{y_1} \\ \Rightarrow y_1=\frac{72\times 10}{3}=240 \end{gathered}$$
$\mathrm{Therefore},x_1=5,x_2=8\mathrm{and}{y}_1=240$