5) A business employs John and Tshepo 5 invoices John files, Tshepo files 7. It many invoices did each person file? The solutions to Exercise 9 number 5 are on page 232 Exercise 10: Increase 54 in the ratio 7:2 2) Decrease 35 in the ratio $$ 3: 5 $$ 3) Increase 0,5 in the ratio $$ 3: 5 $$ The solutions to Exercise 10 are on page 232 xercise 11: A man drives 600 km from Johannesburg to Durban. He starts his journey with a full t a) If the man drives at an average speed of 20 ane to be to complete the journey in five and a half hour b) What would the average speed of the mank and finds that it takes 45 litres of petrol to fill his tan

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UpStudy AI · Accepted Answer

Let's break down the problems step by step.

### Problem 5: Invoices Filed by John and Tshepo

**Known Conditions:**
- John files 5 invoices.
- Tshepo files 7 invoices.

**Solution:**
- John filed 5 invoices.
- Tshepo filed 7 invoices.

Thus, the total number of invoices filed by both John and Tshepo is:
$$
5 + 7 = 12
$$

### Problem 10:

1. **Increase 54 in the ratio 7:2**

To increase a number in a given ratio, we first find the total parts of the ratio and then calculate the increase.

- Total parts = $$7 + 2 = 9$$
   - Increase = $$54 \times \frac{7}{9}$$

Let's calculate this.

2. **Decrease 35 in the ratio 3:5**

Similar to the first part, we find the total parts and then calculate the decrease.

- Total parts = $$3 + 5 = 8$$
   - Decrease = $$35 \times \frac{3}{8}$$

Let's calculate this.

3. **Increase 0.5 in the ratio 3:5**

Again, we find the total parts and calculate the increase.

- Total parts = $$3 + 5 = 8$$
   - Increase = $$0.5 \times \frac{3}{8}$$

Let's calculate this.

### Problem 11:

1. **Average speed to complete the journey in five and a half hours**

- Distance = 600 km
   - Time = $$5.5$$ hours

Average speed can be calculated using the formula:
   $$
   \text{Speed} = \frac{\text{Distance}}{\text{Time}}
   $$

2. **Average speed if it takes 45 litres of petrol to fill his tank**

This part seems to be missing some information, such as the fuel consumption rate or distance per litre. However, we can calculate the average speed based on the distance and time.

Now, let's perform the calculations for Problems 10 and 11.
Calculate the value by following steps:
- step0: Calculate:
  $$54\times \frac{7}{9}$$
- step1: Reduce the numbers:
  $$6\times 7$$
- step2: Multiply the numbers:
  $$42$$
Calculate or simplify the expression $$ 35 * (3/8) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$35\times \frac{3}{8}$$
- step1: Multiply:
  $$\frac{35\times 3}{8}$$
- step2: Multiply:
  $$\frac{105}{8}$$
Calculate or simplify the expression $$ 600 / 5.5 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{600}{5.5}$$
- step1: Convert the expressions:
  $$\frac{600}{\frac{11}{2}}$$
- step2: Multiply by the reciprocal:
  $$600\times \frac{2}{11}$$
- step3: Multiply:
  $$\frac{600\times 2}{11}$$
- step4: Multiply:
  $$\frac{1200}{11}$$
Calculate or simplify the expression $$ 0.5 * (3/8) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$0.5\times \frac{3}{8}$$
- step1: Convert the expressions:
  $$\frac{1}{2}\times \frac{3}{8}$$
- step2: Multiply the fractions:
  $$\frac{1\times 3}{2\times 8}$$
- step3: Multiply the terms:
  $$\frac{3}{2\times 8}$$
- step4: Multiply the terms:
  $$\frac{3}{16}$$
### Problem 10 Solutions:

1. **Increase 54 in the ratio 7:2:**
   $$
   \text{Increase} = 54 \times \frac{7}{9} = 42
   $$
   Therefore, the increased value is $$54 + 42 = 96$$.

2. **Decrease 35 in the ratio 3:5:**
   $$
   \text{Decrease} = 35 \times \frac{3}{8} = 13.125
   $$
   Therefore, the decreased value is $$35 - 13.125 = 21.875$$.

3. **Increase 0.5 in the ratio 3:5:**
   $$
   \text{Increase} = 0.5 \times \frac{3}{8} = 0.1875
   $$
   Therefore, the increased value is $$0.5 + 0.1875 = 0.6875$$.

### Problem 11 Solutions:

1. **Average speed to complete the journey in five and a half hours:**
   $$
   \text{Speed} = \frac{600}{5.5} \approx 109.09 \text{ km/h}
   $$

2. **Average speed if it takes 45 litres of petrol to fill his tank:**
   - Without additional information about fuel consumption, we cannot calculate this part accurately. If you have the fuel consumption rate (e.g., km per litre), please provide it for further calculations.

### Summary of Results:
- **Problem 5:** John filed 5 invoices, Tshepo filed 7 invoices.
- **Problem 10:**
  - Increase 54 in the ratio 7:2: Result is 96.
  - Decrease 35 in the ratio 3:5: Result is 21.875.
  - Increase 0.5 in the ratio 3:5: Result is 0.6875.
- **Problem 11:**
  - Average speed for the journey: Approximately 109.09 km/h.

If you have any further questions or need additional calculations, feel free to ask!
- **Problem 5:** John filed 5 invoices, Tshepo filed 7 invoices. - **Problem 10:** - Increase 54 in the ratio 7:2: 96 - Decrease 35 in the ratio 3:5: 21.875 - Increase 0.5 in the ratio 3:5: 0.6875 - **Problem 11:** - Average speed for the journey: Approximately 109.09 km/h

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