To determine how many tickets Max had at the start, we can follow a few steps to analyze the situation, plan our solution, and justify our result.
Step 1: Analyze the Information
- Initial tickets: Let \( x \) represent the number of tickets Max had at the start.
- Expenditures:
- Spent on carnival ride: 45 tickets
- Spent on game: 19 tickets
- Spent on food: 32 tickets
- Remaining tickets after the expenditures: Max has 16 tickets left.
- Future expenditure: Max plans to spend 10 tickets at skee ball.
Step 2: Plan the Calculation
Using the information above, we can set up an equation to find \( x \):
- Calculate the total amount spent: \[ \text{Total spent} = 45 + 19 + 32 \]
- Substituting what we know into an equation: \[ x - (\text{Total spent}) = 16 \]
- After spending on skee ball (next), we can also express: \[ 16 - 10 \text{ (for skee ball)} \text{ will be the remaining tickets after this expenditure.} \]
Step 3: Solve the Equation
Now, we can calculate the total amount spent: \[ 45 + 19 = 64 \] \[ 64 + 32 = 96 \] Therefore, Max spent a total of 96 tickets on the carnival ride, game, and food.
Now we can plug this total into our equation: \[ x - 96 = 16 \] Adding 96 to both sides gives: \[ x = 16 + 96 \] \[ x = 112 \]
Step 4: Justify and Evaluate the Result
At the start, Max had 112 tickets. We can check whether this makes sense with all the expenditures:
Starting with 112 tickets:
- After spending 45 tickets on the carnival ride: \[ 112 - 45 = 67 \]
- After spending 19 tickets on the game: \[ 67 - 19 = 48 \]
- After spending 32 tickets on food: \[ 48 - 32 = 16 \]
This confirmation shows that after spending on the ride, game, and food, Max indeed has 16 tickets left. If Max then spends 10 on skee ball: \[ 16 - 10 = 6 \] Max would have 6 tickets left.
Thus, the calculations are logically consistent, and the solution is justified.
Conclusion
Max had 112 tickets at the start.