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Sagot :
Sure, let's break down the problem step by step and solve it.
### Part 1: Distribution of Sale Amount for the Boat
Initial Contributions:
1. Greg paid: \[tex]$1050 2. Nigel paid: \$[/tex]1750
3. Mike paid: \[tex]$4200 Total Contribution: To find the total amount paid for the boat: \[ \text{Total Paid} = 1050 + 1750 + 4200 = \$[/tex]7000 \]
Sale Amount:
The boat is sold for \[tex]$3300 after 5 years. Ratio Calculation and Distribution: Each person's share of the sale amount is based on the ratio of their contributions to the total amount paid for the boat. \[ \text{Greg’s Share} = \left(\frac{1050}{7000}\right) \times 3300 = \$[/tex]495.00 \]
[tex]\[ \text{Nigel’s Share} = \left(\frac{1750}{7000}\right) \times 3300 = \$825.00 \][/tex]
[tex]\[ \text{Mike’s Share} = \left(\frac{4200}{7000}\right) \times 3300 = \$1980.00 \][/tex]
### Part 2: Calculation of Losses
Loss Calculation:
To find out how much each person loses, we subtract their share of the sale amount from the amount they initially paid.
[tex]\[ \text{Greg’s Loss} = 1050 - 495 = \$555.00 \][/tex]
[tex]\[ \text{Nigel’s Loss} = 1750 - 825 = \$925.00 \][/tex]
[tex]\[ \text{Mike’s Loss} = 4200 - 1980 = \$2220.00 \][/tex]
Comparative Loss:
To find how much more money Mike lost than Greg, we calculate the difference in their losses.
[tex]\[ \text{Mike’s Loss More Than Greg} = 2220 - 555 = \$1665.00 \][/tex]
### Part 3: Determining the Smallest Loss
Among Greg, Nigel, and Mike, we compare the losses to determine who made the smallest loss.
- Greg’s Loss: \[tex]$555.00 - Nigel’s Loss: \$[/tex]925.00
- Mike’s Loss: \[tex]$2220.00 The smallest loss is Greg’s Loss: \$[/tex]555.00
### Part 4: Distribution of Sweets among Children
Initial Ages:
- Child 1 (youngest): 3 years
- Child 2: 7 years
- Child 3 (oldest): 10 years
Total Sweets:
Patrick distributes 280 sweets among his children based on their ages.
Initial Distribution:
First, we calculate the total age sum:
[tex]\[ \text{Total Age} = 3 + 7 + 10 = 20 \][/tex]
Next, we find how many sweets each child receives based on the ratio of their age to the total age.
[tex]\[ \text{Sweets for Child 1} = \left(\frac{3}{20}\right) \times 280 = 42 \][/tex]
[tex]\[ \text{Sweets for Child 2} = \left(\frac{7}{20}\right) \times 280 = 98 \][/tex]
[tex]\[ \text{Sweets for Child 3} = \left(\frac{10}{20}\right) \times 280 = 140 \][/tex]
Ages after 5 Years:
- Child 1: 3 + 5 = 8 years
- Child 2: 7 + 5 = 12 years
- Child 3: 10 + 5 = 15 years
Revised Distribution:
New total age sum:
[tex]\[ \text{New Total Age} = 8 + 12 + 15 = 35 \][/tex]
[tex]\[ \text{New Sweets for Child 1} = \left(\frac{8}{35}\right) \times 280 = 64 \][/tex]
[tex]\[ \text{New Sweets for Child 2} = \left(\frac{12}{35}\right) \times 280 = 96 \][/tex]
[tex]\[ \text{New Sweets for Child 3} = \left(\frac{15}{35}\right) \times 280 = 120 \][/tex]
Difference in Sweets for the Oldest Child:
The difference in the number of sweets received by the oldest child (Child 3) from now and five years later is:
[tex]\[ \text{Difference} = 140 - 120 = 20 \][/tex]
### Summary of Answers
1. Amount each receives from the sale:
- Greg: \[tex]$495.00 - Nigel: \$[/tex]825.00
- Mike: \[tex]$1980.00 2. Mike loses \$[/tex]1665.00 more than Greg from the sale of the boat.
3. Greg made the smallest loss of \$555.00.
4. The oldest child will receive 20 fewer sweets in five years than she does now.
### Part 1: Distribution of Sale Amount for the Boat
Initial Contributions:
1. Greg paid: \[tex]$1050 2. Nigel paid: \$[/tex]1750
3. Mike paid: \[tex]$4200 Total Contribution: To find the total amount paid for the boat: \[ \text{Total Paid} = 1050 + 1750 + 4200 = \$[/tex]7000 \]
Sale Amount:
The boat is sold for \[tex]$3300 after 5 years. Ratio Calculation and Distribution: Each person's share of the sale amount is based on the ratio of their contributions to the total amount paid for the boat. \[ \text{Greg’s Share} = \left(\frac{1050}{7000}\right) \times 3300 = \$[/tex]495.00 \]
[tex]\[ \text{Nigel’s Share} = \left(\frac{1750}{7000}\right) \times 3300 = \$825.00 \][/tex]
[tex]\[ \text{Mike’s Share} = \left(\frac{4200}{7000}\right) \times 3300 = \$1980.00 \][/tex]
### Part 2: Calculation of Losses
Loss Calculation:
To find out how much each person loses, we subtract their share of the sale amount from the amount they initially paid.
[tex]\[ \text{Greg’s Loss} = 1050 - 495 = \$555.00 \][/tex]
[tex]\[ \text{Nigel’s Loss} = 1750 - 825 = \$925.00 \][/tex]
[tex]\[ \text{Mike’s Loss} = 4200 - 1980 = \$2220.00 \][/tex]
Comparative Loss:
To find how much more money Mike lost than Greg, we calculate the difference in their losses.
[tex]\[ \text{Mike’s Loss More Than Greg} = 2220 - 555 = \$1665.00 \][/tex]
### Part 3: Determining the Smallest Loss
Among Greg, Nigel, and Mike, we compare the losses to determine who made the smallest loss.
- Greg’s Loss: \[tex]$555.00 - Nigel’s Loss: \$[/tex]925.00
- Mike’s Loss: \[tex]$2220.00 The smallest loss is Greg’s Loss: \$[/tex]555.00
### Part 4: Distribution of Sweets among Children
Initial Ages:
- Child 1 (youngest): 3 years
- Child 2: 7 years
- Child 3 (oldest): 10 years
Total Sweets:
Patrick distributes 280 sweets among his children based on their ages.
Initial Distribution:
First, we calculate the total age sum:
[tex]\[ \text{Total Age} = 3 + 7 + 10 = 20 \][/tex]
Next, we find how many sweets each child receives based on the ratio of their age to the total age.
[tex]\[ \text{Sweets for Child 1} = \left(\frac{3}{20}\right) \times 280 = 42 \][/tex]
[tex]\[ \text{Sweets for Child 2} = \left(\frac{7}{20}\right) \times 280 = 98 \][/tex]
[tex]\[ \text{Sweets for Child 3} = \left(\frac{10}{20}\right) \times 280 = 140 \][/tex]
Ages after 5 Years:
- Child 1: 3 + 5 = 8 years
- Child 2: 7 + 5 = 12 years
- Child 3: 10 + 5 = 15 years
Revised Distribution:
New total age sum:
[tex]\[ \text{New Total Age} = 8 + 12 + 15 = 35 \][/tex]
[tex]\[ \text{New Sweets for Child 1} = \left(\frac{8}{35}\right) \times 280 = 64 \][/tex]
[tex]\[ \text{New Sweets for Child 2} = \left(\frac{12}{35}\right) \times 280 = 96 \][/tex]
[tex]\[ \text{New Sweets for Child 3} = \left(\frac{15}{35}\right) \times 280 = 120 \][/tex]
Difference in Sweets for the Oldest Child:
The difference in the number of sweets received by the oldest child (Child 3) from now and five years later is:
[tex]\[ \text{Difference} = 140 - 120 = 20 \][/tex]
### Summary of Answers
1. Amount each receives from the sale:
- Greg: \[tex]$495.00 - Nigel: \$[/tex]825.00
- Mike: \[tex]$1980.00 2. Mike loses \$[/tex]1665.00 more than Greg from the sale of the boat.
3. Greg made the smallest loss of \$555.00.
4. The oldest child will receive 20 fewer sweets in five years than she does now.
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