4.2.3 Ratio, Rates and Proportions, PT3 Focus Practice

Question 8:
Liza received three types of coloured marbles, red, green and yellow in the ratio of 2 : 5 : x. Given that the number of yellow marbles are more than the number of red marbles but less than the number of green marbles.

Calculate the number of yellow marbles that Liza received if the total number of marbles is 120.

Solution:
red : green : yellow = 2 : 5 : x
Given 2 < x < 5, so possible value of x is 3 in order to get a round number from the total of 120 marbles.

$\begin{array}{l}\frac{\text{yellow marbles}}{\text{total marbles}}=\frac{3}{2+5+3}\\ \frac{\text{yellow marbles}}{120}=\frac{3}{10}\\ \text{yellow marbles}=\frac{3}{10}\times 120\\ \text{yellow marbles}=36\end{array}$

Question 9:
John and Mahmud are required to draw a triangle ABC. The ratio of ∠A : ∠B : ∠C of the triangle drawn by John is 4 : 8 : 3 while the triangle drawn by Mahmud is 5 : 5 : 8.

Find the difference between the value of ∠B drawn by John and Mahmud.

Solution:
$\begin{array}{l}\angle B\text{ drawn by John}\\ =\frac{8}{4+8+3}\times {180}^o\\ ={96}^o\\ \\ \angle B\text{ drawn by Mahmud}\\ =\frac{5}{5+5+8}\times {180}^o\\ ={50}^o\end{array}$

Question 10:
The number of workers in an office building is 168 and they are placed in level two and level three. The number of workers in level three is 72.

(a) The ratio of workers in level two to level three is x : 3.
Find the value of x.

(b) 162 new workers have just started working in the office building. 3 of them are placed in level two, 93 in level three, while the rest is placed in level four.
Determine the ratio, in the lowest term of the workers of level two to three to four.

Solution:
$\begin{array}{l}\text{(a)}\\ \text{Ratio of workers in level two to level three}=x:3\\ x:3=\left(168-72\right):72\\ x:3=96:72\\ \frac{x}{3}=\frac{96}{72}\\ x=\frac{96}{72}\times 3\\ x=4\end{array}$

$\begin{array}{l}\text{(b)}\\ \text{Ratio of workers in level two to three to four}\\ =\left(96+3\right):\left(72+93\right):\left(162-3-93\right)\\ =99:165:66\\ =\frac{99}{33}:\frac{165}{33}:\frac{66}{33}\\ =3:5:2\end{array}$