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!
### 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!