https://file.aiquickdraw.com/mathbot/file/1726083084609vzfa2c9y.jpg

The image shows two problems involving proportional relationships. Let's break down each part and solve them.

### (a) Arcade Game: Tickets per Points

The table shows the relationship between points and tickets:
- 3 points → 27 tickets
- 5 points → 45 tickets
- 9 points → 72 tickets

We need to predict the number of tickets for 10 points.

**Step 1: Check if the relationship is proportional.**  
Find the ratio of tickets to points for each row:
- $ \frac{27}{3} = 9 $
- $ \frac{45}{5} = 9 $
- $ \frac{72}{9} = 8 $

Since the ratios are not consistent, the number of tickets per point is not always the same. This leads to the first option:  
- Each point does **not** always give the same number of tickets.

**Step 2: Use the ratios to predict the tickets for 10 points.**  
We observe that the ratios decrease slightly as the number of points increases. Since 9 points give 8 tickets per point, we can approximate using the last ratio:
- $ \frac{72}{9} = 8 $, so for 10 points, we estimate $ 10 \times 8 = 80 $.

**Prediction for 10 points: 80 tickets.**

### (b) Tuna Price: Dollars per Pound

The table shows the price of tuna for different amounts:
- 2 pounds → $10
- 4 pounds → $20
- 7 pounds → $35

We need to predict how many pounds of tuna can be bought for $45.

**Step 1: Check if the price per pound is constant.**  
Find the price per pound:
- $ \frac{10}{2} = 5 $ dollars per pound
- $ \frac{20}{4} = 5 $ dollars per pound
- $ \frac{35}{7} = 5 $ dollars per pound

Since the price per pound is consistent, we select the second option:  
- The price per pound of tuna **appears to be the same**.

**Step 2: Predict the amount for $45.**  
Using the constant price of $5 per pound:
- $ \frac{45}{5} = 9 $ pounds.

**Prediction for $45: 9 pounds of tuna.**

### Final Answers:
- (a) Predicted number of tickets for 10 points: **80 tickets**
- (b) Predicted amount of tuna for $45: **9 pounds**

Do you need any further details or clarifications?  
Here are 5 related questions for further practice:
1. How would you calculate the tickets if the ratio continued decreasing?
2. What would the cost of 12 pounds of tuna be based on the given information?
3. If the price per pound of tuna changes, how would you adjust your calculations?
4. Can you determine a formula for the number of tickets based on points?
5. What would happen if the points-to-tickets ratio stayed constant?

**Tip:** Always check the ratios in a table to determine if the relationship is proportional.

For parts (a) and (b), choose the correct description. (a) A certain arcade game gives players tickets. The table below shows the number of tickets a player gets for the number of points. (b) A local store is selling fresh tuna. The table below shows the price for the amount of tuna.

Learn how to predict the number of tickets in an arcade game and the price of tuna based on ratios and proportions. Understand how to check for proportionality and calculate predictions for both situations. This problem is suitable for students in Grades 6-8.

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