People in Mrs - NSC Mathematical Literacy - Question 4 - 2017 - Paper 2

Calculate the total height of the decorations:

• The total height of the triangular and circular portions is: $75 \text{ cm} + 100 \text{ cm} = 175 \text{ cm} = 1.75 \text{ m}$

Calculate the remaining wall height:

• Thus, the remaining height of the wall is: $4 \text{ m} - 1.75 \text{ m} = 2.25 \text{ m}$

Since the decorations are at equal distances from the top and bottom, divide the remaining height by 2:

• Distance from the top to the decoration: $\text{Distance} = \frac{2.25}{2} = 1.125 \text{ m}$

Calculate the area for red paint:

• Area of the rectangle: $\text{Area}_{rectangle} = 150 \text{ cm} \times 75 \text{ cm} = 11250 \text{ cm}^2$
• Area of one triangle: $\text{Area}_{triangle} = \frac{1}{2} \times 75 \text{ cm} \times 75 \text{ cm} = 2812.5 \text{ cm}^2$
• Total area for two triangles is: $\text{Total Area}_{triangles} = 2 \times 2812.5 = 5625 \text{ cm}^2$
• Overall area to be painted: $\text{Total Area} = 11250 + 5625 = 16875 \text{ cm}^2$

Convert to m²:

• $\text{Total Area} = \frac{16875}{10000} = 1.6875 \text{ m}^2$

Calculate the paint required:

• For 15 decorations: $\text{Total Area}_{15} = 1.6875 \text{ m}^2 \times 15 = 25.3125 \text{ m}^2$

Calculate litres needed:

• Each litre covers 12 m²; hence: $\text{Litres} = \frac{25.3125}{12} \approx 2.1094 \text{ litres}$
• Therefore, need 3 tins of paint (rounding up).

Calculate cost for the paints needed:

• White paint cost:
  • $\text{Cost} = 499 \times 3 = R1497$
• Red paint cost:
  • $\text{Cost} = 505 \times 2 = R1010$

Check Mr. Sibeko's statement:

• Total for red paint:
  • R1010, and for white paint, it’s R1497 (not twice of white). This statement is incorrect.