A resort plans to apportion 5454 new toboggans among the four resorts based on the number of rooms in each resort as shown below. Determine each​ resort's apportionment using​ Adams's method.​ Hint: Some divisor between 1111 and 1212 will work.
Resort
A
B
C
D
Total
 
Number of rooms
9696
115115
141141
242242
594594


Adams's method is an apportionment technique that works by finding a divisor, dividing each resort's number of rooms by that divisor, and rounding **up** to the nearest whole number. The objective is to distribute the total number of toboggans (5454) among the resorts proportionally based on the number of rooms.

### Step-by-Step Solution Using Adams's Method:

1. **Find Total Number of Rooms:**

   Add the number of rooms from all the resorts:

   \[
   969 + 1151 + 1411 + 2422 = 5945
   \]

2. **Estimate a Divisor:**

   Since Adams's method rounds up, we start with the total number of toboggans (5454) and estimate a divisor. According to the hint, it should be between 1111 and 1212. 

   We calculate each resort’s apportionment by dividing the number of rooms by different divisors and rounding up to find the correct one.

### Trying different divisors:

Let's test by trial and error around 1175.

---

#### Divisor = 1175

\[
\text{Resort A} = \frac{969}{1175} = 0.8247 \Rightarrow 1 \text{ (round up)}
\]
\[
\text{Resort B} = \frac{1151}{1175} = 0.9796 \Rightarrow 1 \text{ (round up)}
\]
\[
\text{Resort C} = \frac{1411}{1175} = 1.2009 \Rightarrow 2 \text{ (round up)}
\]
\

A resort plans to apportion 5454 new toboggans among the four resorts based on the number of rooms in each resort as shown below. Determine each​ resort's apportionment using​ Adams's method.​ Hint: Some divisor between 1111 and 1212 will work.

This problem explores how to apportion 5454 new toboggans among four resorts using Adams's method of apportionment. The resorts have varying numbers of rooms, and the solution involves estimating a divisor, dividing, and rounding up. Suitable for high school students in Grades 11-12, this example showcases key mathematical concepts of division and rounding.

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