4.2 Calculate the value of $$ a $$ if: (2) 4.3 increase 5200 kg in the ratio $$ 2: 5 $$ (2) $$ \qquad $$ 4.4 Share 90 sweets in the following ratio $$ 5: 3: 7 $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ (3) $$ \qquad $$ [9] QUESTION 5 5.1 It takes 7 gardeners 8 hours to plant 1680 seedlings on a piece of land. Calculate (in hours and minutes) how long it would take 12 gardeners to plant the same seedlings. $$ \qquad $$ $$ \qquad $$ (2) $$ \qquad $$ 5.2 A car travelling at a constant speed travels 30 km in 15 minutes. How far will it travel in 2 hours 12 minutes if it continues at the same constant speed? $$ \qquad $$ $$ \qquad $$

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UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(\frac{1680}{7}\right)\times 8}{12}$$
- step1: Divide the terms:
  $$\frac{240\times 8}{12}$$
- step2: Multiply the numbers:
  $$\frac{1920}{12}$$
- step3: Reduce the fraction:
  $$160$$
Calculate or simplify the expression $$ 90 * (3/15) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$90\left(\frac{3}{15}\right)$$
- step1: Reduce the fraction:
  $$90\times \frac{1}{5}$$
- step2: Reduce the numbers:
  $$18\times 1$$
- step3: Simplify:
  $$18$$
Calculate or simplify the expression $$ (30 / (15/60)) * (132) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{30}{\left(\frac{15}{60}\right)}\right)\times 132$$
- step1: Remove the parentheses:
  $$\left(\frac{30}{\frac{15}{60}}\right)\times 132$$
- step2: Reduce the fraction:
  $$\left(\frac{30}{\frac{1}{4}}\right)\times 132$$
- step3: Divide the terms:
  $$120\times 132$$
- step4: Multiply the numbers:
  $$15840$$
Calculate or simplify the expression $$ 5200 * (2/5) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$5200\times \frac{2}{5}$$
- step1: Reduce the numbers:
  $$1040\times 2$$
- step2: Multiply the numbers:
  $$2080$$
Calculate or simplify the expression $$ 90 * (5/15) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$90\left(\frac{5}{15}\right)$$
- step1: Reduce the fraction:
  $$90\times \frac{1}{3}$$
- step2: Reduce the numbers:
  $$30\times 1$$
- step3: Simplify:
  $$30$$
Calculate or simplify the expression $$ 90 * (7/15) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$90\times \frac{7}{15}$$
- step1: Reduce the numbers:
  $$6\times 7$$
- step2: Multiply the numbers:
  $$42$$
Calculate or simplify the expression $$ 30 / (15/60) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{30}{\left(\frac{15}{60}\right)}$$
- step1: Remove the parentheses:
  $$\frac{30}{\frac{15}{60}}$$
- step2: Reduce the fraction:
  $$\frac{30}{\frac{1}{4}}$$
- step3: Multiply by the reciprocal:
  $$30\times 4$$
- step4: Multiply the numbers:
  $$120$$
Let's solve each part of the problem step by step.

### 4.3 Increase 5200 kg in the ratio $$ 2: 5 $$

To find the increase in weight, we first need to calculate the total parts in the ratio $$ 2:5 $$:
- Total parts = $$ 2 + 5 = 7 $$

Now, we can find the increase corresponding to the $$ 2 $$ parts:
$$
\text{Increase} = 5200 \times \frac{2}{7} = 2080 \text{ kg}
$$

### 4.4 Share 90 sweets in the ratio $$ 5: 3: 7 $$

First, we calculate the total parts in the ratio $$ 5:3:7 $$:
- Total parts = $$ 5 + 3 + 7 = 15 $$

Now, we can find the number of sweets for each part:
1. For $$ 5 $$ parts:
   $$
   \text{Sweets for 5 parts} = 90 \times \frac{5}{15} = 30
   $$
2. For $$ 3 $$ parts:
   $$
   \text{Sweets for 3 parts} = 90 \times \frac{3}{15} = 18
   $$
3. For $$ 7 $$ parts:
   $$
   \text{Sweets for 7 parts} = 90 \times \frac{7}{15} = 42
   $$

### QUESTION 5

#### 5.1 Calculate how long it would take 12 gardeners to plant 1680 seedlings.

First, we find the total work done in gardener-hours:
$$
\text{Total work} = 7 \text{ gardeners} \times 8 \text{ hours} = 56 \text{ gardener-hours}
$$

Now, we find the time it would take for 12 gardeners:
$$
\text{Time} = \frac{56 \text{ gardener-hours}}{12 \text{ gardeners}} = \frac{56}{12} \text{ hours} = 4.67 \text{ hours} \approx 4 \text{ hours and } 40 \text{ minutes}
$$

#### 5.2 A car travelling at a constant speed travels 30 km in 15 minutes.

First, we calculate the speed of the car:
$$
\text{Speed} = \frac{30 \text{ km}}{15 \text{ minutes}} = 120 \text{ km/hour}
$$

Now, we need to find out how far it will travel in $$ 2 $$ hours and $$ 12 $$ minutes:
- Convert $$ 12 $$ minutes to hours: $$ 12 \text{ minutes} = \frac{12}{60} = 0.2 \text{ hours} $$
- Total time = $$ 2 + 0.2 = 2.2 \text{ hours} $$

Now, we calculate the distance:
$$
\text{Distance} = 120 \text{ km/hour} \times 2.2 \text{ hours} = 264 \text{ km}
$$

### Summary of Results
- Increase in weight: **2080 kg**
- Sweets distribution: **30, 18, 42**
- Time for 12 gardeners: **4 hours and 40 minutes**
- Distance travelled in 2 hours 12 minutes: **264 km**
- **Increase in weight:** 2080 kg - **Sweets distribution:** 30, 18, 42 - **Time for 12 gardeners:** 4 hours and 40 minutes - **Distance travelled in 2 hours 12 minutes:** 264 km

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