**5.2.1 Ratio, Rates and Proportions (I), PT3 Focus Practice**

Question 1:

Question 1:

Given

*x*:*y*= 4 : 5 and*x*+*y*= 180. Find the value of*x*.

Solution:Solution:

**Question 2:**

Given

*x*:*y*= 9 : 5 and*x*–*y*= 16. Find the value of*x*+*y*.

*Solution:***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:Solution:

$\begin{array}{l}\frac{\text{Rizal}}{\text{Amy+Muthu}}=\frac{1}{2+3}\\ \frac{\text{Rizal}}{RM360}=\frac{1}{5}\\ \text{Rizal}=\frac{1}{5}\times RM360\\ \text{}=RM72\end{array}$

**Question 4:**

In the figure,

*TU*:*UV*:*VW*= 5 : 7 : 2.If

*TU*= 30 cm, what is the length of*TW*?

Solution:Solution:

$\begin{array}{l}\text{Given}TU:UV:VW=5:7:2\\ TU=30cm\\ \\ \frac{TU+UV+VW}{TU}=\frac{5+7+2}{5}\\ \frac{TW}{30}=\frac{14}{5}\\ TW=\frac{14}{5}\times 30\\ \text{}=84cm\end{array}$

**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:Solution:

$\begin{array}{l}AB:BC:CA=4:7:6\\ BC=35cm\\ \\ \frac{AB}{BC}=\frac{4}{7}\\ \frac{AB}{35}=\frac{4}{7}\\ AB=\frac{4}{7}\times 35\\ \text{}=20cm\\ \frac{CA}{35}=\frac{6}{7}\\ CA=\frac{6}{7}\times 35\\ \text{}=30cm\end{array}$

Difference in length between

*AB*and

*CA*

= 30 – 20

= 10 cm