High School

1. In a packet of 30 Smarties, there are 8 yellow Smarties. Write the number of yellow Smarties as a percentage of the total.

2. Calculate the scores:
- Renting obtained [tex]\(\frac{22}{5}\)[/tex] in a mathematics literacy test and [tex]\(\frac{18 \times 5}{255}\)[/tex] in a geography test. In which subject did she score the highest?

3. Andrew is able to drive 68 km on a full tank of petrol before needing to refuel. The petrol tank on Andrew's car can hold 10 liters of petrol.

3.1. Write down the fuel consumption rate of Andrew's car in km per liter.

3.2. How many liters of petrol will Andrew's car use to travel 285 km? Round off your answer to one decimal place.

3.3. If Andrew sets out on a trip with 28 liters of petrol, how far will he be able to travel before needing to stop for petrol?

Answer :

Sure! Let's go through the problem step by step and find the solution:

### 1. Percentage of Yellow Smarties

In a packet of 30 Smarties, there are 8 yellow Smarties. To find the percentage of yellow Smarties, use the formula:

[tex]\[
\text{Percentage of yellow Smarties} = \left( \frac{\text{Number of yellow Smarties}}{\text{Total number of Smarties}} \right) \times 100
\][/tex]

Plugging in the values:

[tex]\[
\text{Percentage of yellow Smarties} = \left( \frac{8}{30} \right) \times 100 \approx 26.67\%
\][/tex]

### 2. Highest Score from the Literacy and Geography Tests

#### Math Literacy Test:
The score formula based on fractions is:

[tex]\[
\text{Math score} = \frac{22 \times 5}{301} \times 70
\][/tex]

Simplifying this calculation gives an approximate score of 25.58.

#### Geography Test:
The score formula based on fractions is:

[tex]\[
\text{Geography score} = \frac{18 \times 5}{255}
\][/tex]

Simplifying this calculation gives an approximate score of 0.35.

Comparing the two scores, the Math Literacy Test has the higher score, approximately 25.58.

### 3. Fuel Consumption Calculations for Andrew's Car

#### 3.1. Fuel Consumption Rate

Andrew can drive 68 km on a full tank of 12 liters of petrol. To calculate the fuel consumption rate (in km per liter), use the formula:

[tex]\[
\text{Fuel consumption rate} = \frac{\text{Total distance}}{\text{Full tank liters}}
\][/tex]

[tex]\[
\text{Fuel consumption rate} = \frac{68}{12} \approx 5.67 \text{ km/liter}
\][/tex]

#### 3.2. Liters of Petrol Needed for 285 km

To determine how many liters of petrol Andrew's car will use to travel 285 km, use the fuel consumption rate:

[tex]\[
\text{Liters used} = \frac{\text{Distance to travel}}{\text{Fuel consumption rate}}
\][/tex]

[tex]\[
\text{Liters used} = \frac{285}{5.67} \approx 50.3 \text{ liters}
\][/tex]

### 3.3. Distance Travelable with 28 Liters

Lastly, to find out how far Andrew can travel with 28 liters of petrol, use the fuel consumption rate:

[tex]\[
\text{Distance travelable} = \text{Fuel consumption rate} \times \text{Liters available}
\][/tex]

[tex]\[
\text{Distance travelable} = 5.67 \times 28 \approx 158.67 \text{ km}
\][/tex]

These are the detailed solutions to each part of the problem!