Conversions and Time (Grade 11 NSC Matric Mathematical Literacy): Revision Notes

Worked Example: Sugar Conversion Calculation

Problem: A person buys a 500 g bag of sugar. If a recipe asks for 750 ml of sugar, will this 500 g bag be big enough or will more sugar need to be bought?

Solution: Using the conversion factor that 4 g of sugar = 5 ml:

Step 1: Set up the conversion ratio $4 \text{ g} \rightarrow 5 \text{ ml}$

Step 2: Find the conversion for 1 g $1 \text{ g} \rightarrow \frac{5}{4} \text{ ml}$

Step 3: Calculate for 500 g $500 \text{ g} \rightarrow \frac{5}{4} \times 500 = 625 \text{ ml}$

Answer: The 500 g bag only provides 625 ml of sugar, but the recipe needs 750 ml. Therefore, more sugar needs to be bought.

Alternative method: Work from volume to weight $5 \text{ ml} \rightarrow 4 \text{ g}$ $1 \text{ ml} \rightarrow \frac{4}{5} \text{ g}$ $750 \text{ ml} \rightarrow \frac{4}{5} \times 750 = 600 \text{ g}$

This shows that 750 ml requires 600 g of sugar, but we only have 500 g available.

Worked Example: Paint Coverage Calculation

Problem: A wall has dimensions of approximately 6 m by 5 m. The painter estimates the surface area is 30 m². The paint has a conversion factor (spread rate) of 9 m² per litre. How many litres of paint might the painter need?

Solution: Step 1: Identify the spread rate $9 \text{ m}^2 \rightarrow 1 \text{ litre}$

Step 2: Find coverage for 1 m² $1 \text{ m}^2 \rightarrow \frac{1}{9} \text{ litre}$

Step 3: Calculate for 30 m² $30 \text{ m}^2 \rightarrow \frac{1}{9} \times 30 = 3.33 \text{ litres}$

Answer: The painter will need more than 3 litres, so should buy at least 4 full litres. The actual quantity may depend on available tin sizes (e.g., 1 litre tin or 5 litre tin).

Worked Example: Paint Quantity Calculation

Problem: If you need to paint 51.2 m² of wall surface using undercoat that covers 7 m² per litre, how much paint do you need?

Solution: Step 1: Use the coverage rate $7 \text{ m}^2 \rightarrow 1 \text{ litre}$

Step 2: Calculate for the required area $51.2 \text{ m}^2 \rightarrow \frac{51.2}{7} = 7.31 \text{ litres}$

Answer: You need approximately 7.31 litres of undercoat.