Answer
- **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
Solution
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**
Answered by UpStudy AI and reviewed by a Professional Tutor

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