Answer :
Let's solve each part of the problem step-by-step.
Map Scale Problem:
The scale of the map is given as 1:500,000. This means that 1 cm on the map represents 500,000 cm in real life.
To find the actual distance corresponding to 23.7 cm on the map:
First, convert the distance from the map to actual distance:
[tex]\text{Actual distance in cm} = 23.7 \text{ cm} \times 500,000 = 11,850,000 \text{ cm}[/tex]
Since 1 km = 100,000 cm, convert the distance to kilometers:
[tex]\text{Actual distance in km} = \frac{11,850,000}{100,000} = 118.5 \text{ km}[/tex]
Time Calculation for Baking a Cake:
The cake was baked from 11:20:00 to 12:05:30.
Calculate the difference in hours, minutes, and seconds:
[tex]\text{Start time} = 11:20:00 \\
\text{End time} = 12:05:30[/tex]Difference:
From 11:20 to 12:00 is 40 minutes, and then from 12:00 to 12:05:30 is 5 minutes and 30 seconds.
Total time taken = 40 minutes + 5 minutes + 30 seconds = 45 minutes and 30 seconds.
Cost and Sheets of Printing Paper:
1.9.1 Calculate the number of sheets in ONE box:
- There are 5 reams in a box, with each ream consisting of 500 sheets.
Therefore, the total number of sheets:
[tex]5 \text{ reams} \times 500 \text{ sheets/ream} = 2500 \text{ sheets}[/tex]
1.9.2 Calculate the cost of ONE sheet:
- The cost of one box is R269, and there are 2500 sheets in a box.
To find the cost per sheet:
[tex]\text{Cost per sheet} = \frac{269}{2500} = R0.1076\dots[/tex]
- Converting this to cents (since 1 Rand = 100 cents):
[tex]\text{Cost per sheet in cents} \approx 10.76 \text{ cents}[/tex]
Thus, the actual distance on the map is 118.5 km, the cake baking time is 45 minutes and 30 seconds, there are 2500 sheets in a box, and the cost of one sheet is approximately 10.76 cents.
