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Here’s the breakdown of the solution to the problems from the image you provided:

### 1. **Final cost of the watch with sales tax:**
   - Watch price = $49.00
   - Sales tax = 7%
   - To find the final cost, you calculate the sales tax and add it to the original price:
   \[
   \text{Sales tax} = 49 \times \frac{7}{100} = 3.43
   \]
   \[
   \text{Final cost} = 49 + 3.43 = 52.43
   \]
   **Answer: $52.43**

### 2. **Next number in the sequence (8, 9, 12, 17, 24, \_):**
   - First, observe the pattern of differences between consecutive terms:
     - $ 9 - 8 = 1 $
     - $ 12 - 9 = 3 $
     - $ 17 - 12 = 5 $
     - $ 24 - 17 = 7 $
   - The differences are increasing by 2 each time (1, 3, 5, 7...).
   - The next difference should be $ 9 $.
   \[
   24 + 9 = 33
   \]
   **Answer: 33**

### 3. **Net gain or loss for the Falcons:**
   - They gained 33 yards but had a penalty of -15 yards.
   \[
   \text{Net gain or loss} = 33 + (-15) = 18
   \]
   **Answer: 18 yards net gain**

### 4. **David’s balance after writing checks:**
   - Initial balance = $24
   - He writes checks for $6, $13, and $36. Let's calculate the total amount of the checks:
   \[
   6 + 13 + 36 = 55
   \]
   - Subtract this from his initial balance:
   \[
   24 - 55 = -31
   \]
   **Answer: -$31 (David is overdrawn by $31)**

### 5. **Swimming calories calculation:**
   - Swimming burns 10 calories per minute.
   - Ivan consumes 350 calories, so he needs to burn the same amount through swimming.
   \[
   \text{Time required to burn 350 calories} = \frac{350}{10} = 35 \text{ minutes}
   \]
   **Answer: 35 minutes**

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Would you like more detailed steps or explanations for any of these problems?

### Related Questions:
1. How do you calculate percentages in general, like in problem 1?
2. What other sequences follow a similar increasing difference pattern as problem 2?
3. What are some common yard penalties in football, and how are they applied to net yardage?
4. How can David avoid an overdraft in his checking account based on problem 4?
5. What other forms of exercise burn calories at similar or higher rates than swimming?

### Tip:
For percentage problems, always start by converting the percentage into a decimal before multiplying it with the base value. This simplifies the calculation!

What is the final cost of a watch that sells for $49.00 if the sales tax is 7%? In the following sequence, (8, 9, 12, 17, 24, _), what is the next number? The Falcons received a penalty of -15 yds after they made a 33 yd gain. What was the net gain or loss for the team? David has $24 in his checking account. If he writes checks for $6, $13, and $36, what will be the balance in his account? Swimming uses up 10 calories of energy per minute. If Ivan wants to expend the same number of calories in swimming that he takes in by eating a 350-calorie snack, how long would he have to swim?

This guide covers a variety of math problems for middle school students, including calculating the final cost of an item with sales tax, identifying the next number in an arithmetic sequence, determining the net gain or loss after a penalty, and basic subtraction in checking account balances.

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