Answer :
Sure! Let's go through each part of the question step by step:
### 2.1.1 Increase R68 in the ratio 7:4
1. Understand the Ratio: The ratio 7:4 means for every 4 parts of the original there are now 7 parts in total. This means you're increasing something by a factor that reflects the difference in these parts.
2. Calculate the Increased Amount:
- First, determine the multiplication factor by dividing the new total parts (7) by the original total parts (4).
- Multiply the original amount (68) by this factor to get the increased amount.
- [tex]\[\text{Increased Amount} = 68 \times \left(\frac{7}{4}\right) = 119.0\][/tex]
### 2.1.2 Decrease 71x in the ratio 5:7
1. Understand the Ratio: The ratio 5:7 indicates for every 7 parts initially, you now have 5 parts after decreasing. This implies a reduction.
2. Calculate the Decreased Amount:
- Determine the multiplication factor by dividing the remaining parts (5) by the original total parts (7).
- Multiply the original amount (71) by this factor to get the decreased amount.
- [tex]\[\text{Decreased Amount} = 71 \times \left(\frac{5}{7}\right) \approx 50.71\][/tex]
### 1.3 Divide 182 kg in the ratio 2:3:8
1. Understand the Ratio: The ratio 2:3:8 means dividing the total into three parts where the first part gets 2 parts, the second gets 3 parts, and the third gets 8 parts.
2. Calculate Each Part:
- First, calculate the total number of parts by adding the ratio numbers: [tex]\(2 + 3 + 8 = 13\)[/tex].
- Compute each part by dividing the total amount (182 kg) by the total number of parts (13) and then multiplying by each individual ratio number:
- [tex]\[\text{Part 1} = 182 \times \left(\frac{2}{13}\right) = 28.0\, \text{kg}\][/tex]
- [tex]\[\text{Part 2} = 182 \times \left(\frac{3}{13}\right) = 42.0\, \text{kg}\][/tex]
- [tex]\[\text{Part 3} = 182 \times \left(\frac{8}{13}\right) = 112.0\, \text{kg}\][/tex]
Thus, the final answers are:
- The increased amount is 119.0.
- The decreased amount is approximately 50.71.
- The parts of 182 kg are 28.0 kg, 42.0 kg, and 112.0 kg.
### 2.1.1 Increase R68 in the ratio 7:4
1. Understand the Ratio: The ratio 7:4 means for every 4 parts of the original there are now 7 parts in total. This means you're increasing something by a factor that reflects the difference in these parts.
2. Calculate the Increased Amount:
- First, determine the multiplication factor by dividing the new total parts (7) by the original total parts (4).
- Multiply the original amount (68) by this factor to get the increased amount.
- [tex]\[\text{Increased Amount} = 68 \times \left(\frac{7}{4}\right) = 119.0\][/tex]
### 2.1.2 Decrease 71x in the ratio 5:7
1. Understand the Ratio: The ratio 5:7 indicates for every 7 parts initially, you now have 5 parts after decreasing. This implies a reduction.
2. Calculate the Decreased Amount:
- Determine the multiplication factor by dividing the remaining parts (5) by the original total parts (7).
- Multiply the original amount (71) by this factor to get the decreased amount.
- [tex]\[\text{Decreased Amount} = 71 \times \left(\frac{5}{7}\right) \approx 50.71\][/tex]
### 1.3 Divide 182 kg in the ratio 2:3:8
1. Understand the Ratio: The ratio 2:3:8 means dividing the total into three parts where the first part gets 2 parts, the second gets 3 parts, and the third gets 8 parts.
2. Calculate Each Part:
- First, calculate the total number of parts by adding the ratio numbers: [tex]\(2 + 3 + 8 = 13\)[/tex].
- Compute each part by dividing the total amount (182 kg) by the total number of parts (13) and then multiplying by each individual ratio number:
- [tex]\[\text{Part 1} = 182 \times \left(\frac{2}{13}\right) = 28.0\, \text{kg}\][/tex]
- [tex]\[\text{Part 2} = 182 \times \left(\frac{3}{13}\right) = 42.0\, \text{kg}\][/tex]
- [tex]\[\text{Part 3} = 182 \times \left(\frac{8}{13}\right) = 112.0\, \text{kg}\][/tex]
Thus, the final answers are:
- The increased amount is 119.0.
- The decreased amount is approximately 50.71.
- The parts of 182 kg are 28.0 kg, 42.0 kg, and 112.0 kg.
