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The Grade 8 learners decided to start living more healthily. They will either jog or cycle There are 125 Grade 8 learners and they jog and cycle in the ratio \( 3: 2 \). Calculate how learners participate in each sport? 4 Jannie receives R150 pocket money per month. In the new year his mother decided to increase his pocket money in the ratio \( 6: 5 \). Calculate Jannie's adjusted monthly pocket money. 5 Khaya is delivering groceries to his mother who stays 8 km from the shop. How long wil take him to cover this distance if he drives at an average speed of \( 65 \mathrm{~km} / \mathrm{h} \) ? Give your a rounded to the nearest minute.

Ask by Carter Warner. in South Africa
Mar 20,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

- **Jogging Learners:** 75 - **Cycling Learners:** 50 - **Jannie's New Pocket Money:** R180 - **Khaya's Travel Time:** Approximately 7 minutes

Solution

### 1. Jogging and Cycling Learners Let the number of learners who jog be \(3x\) and the number who cycle be \(2x\). Since there are 125 learners in total, we have: \[ 3x + 2x = 125 \] \[ 5x = 125 \] \[ x = 25 \] Now, calculate the numbers: - Jogging: \(3 \times 25 = 75\) - Cycling: \(2 \times 25 = 50\) ### 2. Jannie's Adjusted Pocket Money Jannie’s original pocket money is R150. His mother increases his pocket money in the ratio \(6:5\), which means the new amount is obtained by multiplying R150 by \(\frac{6}{5}\). \[ \text{New pocket money} = 150 \times \frac{6}{5} = 150 \times 1.2 = 180 \] ### 3. Khaya's Travel Time Khaya needs to cover a distance of 8 km at an average speed of \(65\, \text{km/h}\). The time taken is calculated by: \[ \text{Time in hours} = \frac{\text{Distance}}{\text{Speed}} = \frac{8}{65} \] Converting this time to minutes: \[ \text{Time in minutes} = \frac{8}{65} \times 60 \approx 7.38\, \text{minutes} \] Rounded to the nearest minute, it will take approximately 7 minutes.

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Bonus Knowledge

In the case of the Grade 8 learners, with a total of 125 students participating in jogging and cycling in a \(3:2\) ratio, you can break it down into parts. For every 5 parts (3 parts jogging and 2 parts cycling), you have \(125 \div 5 = 25\). Therefore, \(3 \times 25 = 75\) learners will jog, while \(2 \times 25 = 50\) will cycle. Health goals achieved, one run/cycle at a time! Now, talking about Jannie's pocket money, with his monthly allowance rising in the ratio of \(6:5\), if his initial amount is R150, you can think of it as multiplying the old one by \(\frac{6}{5}\) to find the new amount. So, \(150 \times \frac{6}{5} = 180\). Jannie's new monthly allowance is R180—a little extra for saving or spending! As for Khaya’s grocery run, the distance to cover is 8 km and at a speed of \(65 \text{ km/h}\), you can find time by using the formula of time = distance ÷ speed. That works out to be \(8 \div 65 \approx 0.123\) hours. Converting hours into minutes means multiplying by 60, giving you about \(7.4\) minutes. So, Khaya will take approximately 7 minutes to reach his mother’s place—plenty of time for a quick chat along the way!

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