7.2.2 Algebraic Formulae, PT3 Practice


Question 6:
Given 2ab=3a b 2 2 . Express a in terms of b.

Solution:
2ab=3a b 2 2 3a2ab= b 2 2 a( 32b )= b 2 2 a= b 2 2( 32b )


Question 7:
Given a= b+1 a . Express b in terms of a.

Solution:
a= b+1 a b+1 = a 2 [ ( b+1 ) 1 2 ] 2 = ( a 2 ) 2 b+1= a 4 b= a 4 1


Question 8:
Given x= 5w 2wy . (i) Express w in terms of x and y. (ii) Find the value of w when x=10 and y=15.

Solution:
(i) x= 5w 2wy 2wxxy=5w 2wx5w=xy w( 2x5 )=xy w= xy 2x5 (ii) w= ( 10 )( 15 ) 2( 10 )5   = 150 15   =10


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

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