High School

3.1 Bokang got 27 out of 30 on his Mathematical Literacy test. He calculated his percentage and found that he got 0.9%. Is his percentage correct?
- If yes, give a reason for your answer.
- If no, give a reason for your answer and show the correct answer.

3.2 Thabo and his friend Amon shared a job of cleaning Thabo's uncle's yard. He paid both of them R400. Thabo worked for three hours, and Amon worked for two hours.
3.2.1 Determine the amount Thabo will receive, if they decide to share the R400 in a ratio of 3:2 respectively.
3.2.2 Thabo used \(\frac{1}{5}\) of his money towards a second hand video game. Calculate how much the video game costs.
3.2.3 Thabo's transport fare to school has increased from R800 to R1 150. Determine the percentage increase of the transport fare.
You may use the formula: Percentage increase = \(\frac{New amount - Old amount}{Old amount} \times 100\)

Answer :

3.1 Bokang's calculation of his test percentage as 0.9% is incorrect.

To calculate the percentage score:

We use the formula:
[tex]\text{Percentage} = \left(\frac{\text{Score obtained}}{\text{Total score possible}}\right) \times 100[/tex]

Substituting Bokang's scores:
[tex]\text{Percentage} = \left(\frac{27}{30}\right) \times 100 = 90\%[/tex]

Therefore, Bokang's correct test percentage is 90%.

3.2 Given that Thabo and Amon were paid [tex]R400[/tex] and they worked in a ratio of 3:2:

3.2.1 To find Thabo's share:

The ratio 3:2 means that for every 5 hours (3 + 2), Thabo gets 3 parts and Amon gets 2 parts.

First, calculate the total parts:
[tex]\text{Total parts} = 3 + 2 = 5[/tex]

Calculate the value of one part:
[tex]\text{One part value} = \frac{400}{5} = 80[/tex]

Thabo's share:
[tex]\text{Thabo's share} = 3 \times 80 = R240[/tex]

3.2.2 To calculate how much Thabo spent on a video game:

Thabo used [tex]\frac{1}{5}[/tex] of his money for the video game.

[tex]\text{Video game cost} = \frac{1}{5} \times 240 = R48[/tex]

3.2.3 To determine the percentage increase in Thabo's transport fare:

Using the formula for percentage increase:
[tex]\text{Percentage increase} = \left(\frac{\text{New amount} - \text{Old amount}}{\text{Old amount}}\right) \times 100[/tex]

Substitute the given values:
[tex]\text{Percentage increase} = \left(\frac{1150 - 800}{800}\right) \times 100[/tex]
[tex]\text{Percentage increase} = \left(\frac{350}{800}\right) \times 100 = 43.75\%[/tex]

Therefore, the increase in Thabo's transport fare is 43.75%.

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