## Problem Solving

 5.1 Problem Solving

 EXAMPLE 1

Here is Farid's height and mass.

Height: $$1.4\text{ m}$$

Weight: $$36\text{ kg}$$

Does Farid have an ideal body mass?

 BMI $$(\text{ kg/m}^2)$$ You have: $$<18.5$$ underweight $$18.5-24.9$$ ideal weight $$25-30$$ overweight $$30$$ or more obes

$$\text{BMI } = \dfrac{\text{Body mass (kg)}}{\text{Height (m)}\times \text{Height(m)}}\\\ \\ \quad\space\space\space=\dfrac{36}{1.4\times 1.4}\\\ \\ \quad\space\space\space=\dfrac{36}{1.96}\\\ \\ \quad\space\space\space=18.37$$

Farid's BMI is $$18.37\text{ kg/m}^2$$. Therefore, Farid has ideal body mass.

 EXAMPLE 2

The picture below shows the volume of water in two containers, R and S.

Mrs Jim wants to prepare some syrup. She dissolves 180 g of sugar in container R. How much sugar, in g, should be dissolved in container S so that both the containers have the same concentration of syrup?

Container R: $$1\dfrac{1}{2}\,m\ell=1500\,\ell$$

$$1\ 500\ ml$$ → $$180\ g$$

$$1\ ml$$ → $$\dfrac{180\ g}{1500\ ml}$$

$$450\ ml$$ → $$\dfrac{180\ g}{1500\ ml}\times450\ ml=54\ g$$

 EXAMPLE 3

Maria’s body mass is 68 kg. She is obese based on her mass, height and age. She tried to reduce her body mass by cycling 3 km and jogging 2.5 km every day for four weeks. Then, her body mass decreased by 5%. Calculate Maria’s new body mass.

SOLUTION:

Original mass = 100%

New mass = 100% - 5% = 95%

$$\dfrac{95}{100}\times\ 68\ kg=0.95\times 68\ kg$$

\begin{aligned}\\ \small{\color{red}5}\space\space\space\small{\color{red}3}\quad\space\space\space\space\\ \small{\color{red}7}\space\space\space\small{\color{red}4}\quad\space\space\space\space\\ \quad0\space.\space9\space5\quad\\ \underline{\times\quad\space\space\space6\space8\space kg}\\ \small{\color{red}1}\quad\quad\quad\space\space\space\space\\ \space\space\space\space7\space\space6\space\space0\space\space\space\space\space\\ \underline{+\space5\space\space7\space\space0\space\space0\quad\space}\\ \underline{\space\space\space6\space\space4\space.6\space\space0\space kg\space}\\ \end{aligned}\\

 EXAMPLE 4

Puan Ina buys a piece of cloth measuring 14 m in length that costs RM 210. The cloth is cut into 7 pieces of equal lengths. She uses 3 pieces of the cloth to make a tablecloth. What is the length of cloth, in m, used to make the tablecloth? Calculate the cost of the tablecloth.

SOLUTION:

The length of the tablecloth:
\begin{aligned}\\ \small{\color{red}2}\quad\quad\quad\quad\quad\quad\quad\\ \dfrac{3}{\cancel7}\times\cancel{14}\ m=3\times2\ m\\ \small{\color{red}1}\quad\quad\quad\quad\quad\quad\quad\quad\quad\\ \quad\quad= 6\ m\quad\space\space\\ \end{aligned}\\

The cost of the tablecloth:
\begin{aligned}\\ \small{\color{red}{\text{RM }30}}\quad\quad\quad\quad\quad\quad\quad\quad\space\space\\ \dfrac{3}{\cancel7}\times\cancel{\text{RM }210}=3\times \text{RM }30\\ \small{\color{red}1}\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\ \quad\quad= \text{RM }\ 90\quad\space\\ \end{aligned}\\