5.2 Ratio, Rates and Proportions (I), PT3 Focus Practice


5.2 Ratio, Rates and Proportions (I), PT3 Focus Practice
Question 1:
Given x : y = 4 : 5 and x + y = 180. Find the value of x.

Solution:
Given x : y = 4 : 5 and x + y = 180 x x + y = 4 4 + 5 x 180 = 4 9 x = 4 9 × 180 = 80
 


Question 2:
Given x : y = 9 : 5 and xy = 16. Find the value of x + y.

Solution:
Given x : y = 9 : 5 and x y = 16 x + y x y = 9 + 5 9 5 x + y 16 = 14 4 x + y = 7 2 × 16 = 56 x + y = 56


Question 3:
Amy, Rizal and Muthu donated to a charity fund in the ratio of 2 : 1 : 3. The total donation from Amy and Muthu was RM360.
Calculate the amount donated by Rizal.

Solution:
Amy : Rizal : Muthu = 2 : 1 : 3
Rizal Amy + Muthu = 1 2 + 3 Rizal R M 360 = 1 5 Rizal = 1 5 × R M 360 = R M 72


Question 4:
In the figure, TU: UV : VW = 5 : 7 : 2.
 
If TU = 30 cm, what is the length of TW?

Solution:
Given T U : U V : V W = 5 : 7 : 2 T U = 30 c m T U + U V + V W T U = 5 + 7 + 2 5 T W 30 = 14 5 T W = 14 5 × 30 = 84 c m


Question 5:
In diagram below, ABC is a triangle.
The sides of the triangle are in the ratio AB : BC: CA = 4 : 7 : 6.
Find the difference in length, in cm, between AB and CA.

Solution:
A B : B C : C A = 4 : 7 : 6 B C = 35 c m A B B C = 4 7 A B 35 = 4 7 A B = 4 7 × 35 = 20 c m C A 35 = 6 7 C A = 6 7 × 35 = 30 c m
Difference in length between AB and CA
= 30 – 20
= 10 cm

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