PT3 Mathematics 2017, Question 8

Question 8 (a):
Diagram 8 shows packets A, B and C that are filled with flour according to the stated mass.

Based on Diagram 8,
(i) State the heaviest mass of flour.
(ii) Puan Chan needs 2.6 kg of flour to bake cakes.
State the two combination of containers that should be chosen in order for her to bake the cakes.

Solution:
(i)
$\begin{array}{l}\text{Container }A=1\text{ kg 80 g}\\ \text{Container }B=1.52\text{ kg }=1\text{ kg 520 g}\\ \text{Container }C=1\frac{1}{2}\text{ kg }=1\text{ kg 500 g}\\ \\ \text{The heaviest mass of flour}\\ =B:1.52\text{ kg}\end{array}$

(ii)
$\begin{array}{l}A=1\text{ kg 80 g}=1.080\text{ kg}\\ B=1.52\text{ kg}\\ C=1\frac{1}{2}\text{ kg }=1.50\text{ kg}\\ \\ \text{Two combination of containers that}\\ \text{should be chosen to bake cake}\\ =1.080\text{ kg}+1.52\text{ kg}\\ =2.6\text{ kg}\\ =\text{ Container }A+\text{container }B\end{array}$

Question 8 (b):
$\text{Simplify }\frac{pq-3q}{5q}÷\frac{p^2-9}{15}$

Solution:
$\begin{array}{l}\frac{pq-3q}{5q}÷\frac{p^2-9}{15}\\ =\frac{pq-3q}{5q}\times \frac{15}{p^2-9}\\ =\frac{\cancel{q}\cancel{\left(p-3\right)}}{\cancel{5}\cancel{q}}\times \frac{{\cancel{15}}^3}{\cancel{\left(p-3\right)}\left(p+3\right)}\\ =\frac{3}{p+3}\end{array}$