Sure! Let's solve this step by step.
### Step 1: Define the Prices and Total Amount
1. The teenager has \($100.
2. The prices of the tops are $\)20 and \($40.
### Step 2: Determine Possible Combinations
We'll find the combinations of tops that add up to exactly $\)100.
#### Combinations:
- If she buys tops costing \($20 each:
- $\)100 / \($20 = 5 tops can be bought.
- If she buys tops costing $\)40 each:
- \($100 / $\)40 = 2.5 tops.
- Since she can't buy a half top, the maximum number of tops costing \($40 she can buy is 2.
### Step 3: List Viable Combinations
Now let's list out all the possible combinations of tops costing $\)20 and \($40 that total exactly $\)100.
1. \(\(1 \text{ top of } \$20 \text{ and } 2 \text{ tops of } \$40 \)\)
2. \(\( 3 \text{ tops of } \$20 \text{ and } 1 \text{ top of } \$40 \)\)
3. \(\( 5 \text{ tops of } \$20 \text{ and } 0 \text{ tops of } \$40 \)\)
So the possible sequences are:
\(\[ (1, 2), (3, 1), (5, 0) \]\)
Where the first number represents the number of \\($20 tops and the second number represents the number of \$\)40 tops.
### Step 4: Determine the Specific Event
We need to find the event where she buys exactly 3 tops costing \($20.
From the possible sequences, we can see:
\[ (3, 1) \]
This means that she can have exactly 3 tops costing $\)20 and, in this scenario, she will also buy 1 top costing \($40.
### Step 5: Draw the Tree (Conceptual)
To represent these possibilities in a tree form visually:
1. Start with $\)100.
2. Create branches for each possible purchase:
- Branch 1: Buy a \($20 top
- Branch 2: Buy a $\)40 top
3. Continue branching out until the total expenditure reaches \($100.
Example:
```
Initial: $\)100
/ \
\($80 $\)60
/ \ / \
\($60 $\)40 \($40 $\)20
...continue until \($0 is left
```
### Summary:
- The possible sequences of prices she could choose are \((1, 2), (3, 1), (5, 0)\).
- The event where she chooses exactly 3 tops costing $\)20 is represented by the sequence \(\((3, 1)\)\). This indicates she buys 3 tops costing \($20 and 1 top costing $\)40.
