# 7.2.2 Algebraic Formulae, PT3 Practice

Question 6:

Solution:
$\begin{array}{l}2ab=3a-\frac{{b}^{2}}{2}\\ 3a-2ab=\frac{{b}^{2}}{2}\\ a\left(3-2b\right)=\frac{{b}^{2}}{2}\\ a=\frac{{b}^{2}}{2\left(3-2b\right)}\end{array}$

Question 7:

Solution:
$\begin{array}{l}a=\frac{\sqrt{b+1}}{a}\\ \sqrt{b+1}={a}^{2}\\ {\left[{\left(b+1\right)}^{\frac{1}{2}}\right]}^{2}={\left({a}^{2}\right)}^{2}\\ b+1={a}^{4}\\ b={a}^{4}-1\end{array}$

Question 8:

Solution:

Question 9:
Azmin is h years old. His father is twice his brother’s age. If Azmin is 3 years older than his brother, write a formula for the sum (S) of their age.

Solution:
Azmin’s age = h
Azmin’s brother’s age = h – 3
Azmin’s father’s age = (h – 3) × 2 = 2h – 6

Therefore, the sum (S) of their age
S = h + (h – 3) + (2h – 6)
S = h + h – 3 + 2h – 6
S = 4h – 9

Question 10:
Mei Ling is 12 years older than Ali. In the next four years, Raju will be two times older than Ali. If h represents Ali’s age, write the algebraic expressions that represent the total of their ages, in terms of h, in four years time.

Solution:
Ali’s age in the next four years = h + 4
Mei Ling’s age = (h + 4) + 12 = h + 16
Raju’s age = (h + 4) × 2 = 2h + 8

Therefore, the total (S) of their age
S = (h + 4) + (h + 16) + (2h + 8)
S = 4h + 28