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How much does each of them receive from the sale of the boat?

Greg, Nigel, and Mike buy a boat. The information below shows how much each of them paid towards the boat.

\begin{tabular}{ll}
5th August 2012 & [tex]$\$[/tex] 1400[tex]$ \\
Greg paid: & $[/tex]\[tex]$ 1050$[/tex] \\
Nigel paid: & [tex]$\$[/tex] 1750[tex]$ \\
Mike paid: & $[/tex]\[tex]$ 4200$[/tex]
\end{tabular}

Five years later, they sell the boat for [tex]$\$[/tex] 3300$. They share the money from the sale of the boat in the same ratio as they paid for it.

1. How much does each of them receive from the sale of the boat?
2. How much more money did Mike lose from the sale of the boat than Greg?
3. Who made the smallest loss from the sale of the boat? How much did he lose?

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At the start of every year, Patrick shares 280 sweets between his children in the ratio of their ages. This year the children are aged 3, 7, and 10.

1. How many fewer sweets will the oldest child receive in five years' time than she receives now?



Answer :

GinnyAnswer
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.

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