(a) Suppose that there were 11 candy bars in the box. Given that Bob did homework for a total of 54 minutes, Peter did homework for a total of 243 minutes, and Ron did homework for a total of 703 minutes, apportion the 11 candy bars among the children using Hamilton’s method. (b) Suppose that before mom hands out the candy bars, the children decide to spend a “little” extra time on homework. Bob puts in an extra 2 minutes (for a total of 56 minutes), Peter an extra 12 minutes (for a total of 255 minutes), and Ron an extra 86 minutes (for a total of 789 minutes). Using these new totals, apportion the 11 candy bars among the children using Hamilton’s method. (c) The results of (a) and (b) illustrate one of the paradoxes of Hamilton’s method. Which one? Explain.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
(a) Suppose that there were 11 candy bars in the box. Given
that Bob did homework for a total of 54 minutes,
Peter did homework for a total of 243 minutes, and
Ron did homework for a total of 703 minutes, apportion
the 11 candy bars among the children using
Hamilton’s method.
(b) Suppose that before mom hands out the candy bars,
the children decide to spend a “little” extra time on
homework. Bob puts in an extra 2 minutes (for a total
of 56 minutes), Peter an extra 12 minutes (for a total
of 255 minutes), and Ron an extra 86 minutes (for a total
of 789 minutes). Using these new totals, apportion the
11 candy bars among the children using Hamilton’s
method.
(c) The results of (a) and (b) illustrate one of the paradoxes
of Hamilton’s method. Which one? Explain.
a). Total number of hours spent on homework:
Number of candy bars=10
Standard Divisor:
The table according to Hamilton's method:
| Child | Minutes spent on homework | Standard Quota | Lower quota | Residue | Order of surplus | Apportionment |
| Bob | 54 | 0 | 0.54 | First | 1 | |
| Peter | 243 | 2 | 0.43 | 2 | ||
| Ron | 703 | 7 | 0.03 | 7 | ||
| Total | 1000 | 10 | 9 | 1 | 10 |
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