https://file.aiquickdraw.com/mathbot/file/1728649738388ufkvwhew.jpg

Let's go through each of the exercises in the image you uploaded. Here's a breakdown of what each task involves:

### **Opgave 1** (Problem 1):
Peter buys several items for his trip:
- A travel pillow: 199 DKK
- 3 pairs of socks: 3 × 58.50 DKK
- 3 rolls of toilet paper: 3 × 39.99 DKK

**Questions:**
a) What is the total cost?
b) If Peter pays with a 500 DKK bill, how much change does he receive?

**Solution for a)**:
- Pillow: 199 DKK
- Socks: 3 × 58.50 = 175.50 DKK
- Toilet paper: 3 × 39.99 = 119.97 DKK

Total cost:  
\( 199 + 175.50 + 119.97 = 494.47 \) DKK

**Solution for b)**:  
If Peter pays with 500 DKK, his change is:  
\( 500 - 494.47 = 5.53 \) DKK

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### **Opgave 2** (Problem 2):
A teacher is at a café. Prices are as follows:
- Danish water: 15 DKK
- Roll with butter: 37 DKK
- Soda water: 25 DKK
- Optional cake: 23 DKK
- Ice cream with sprinkles: 27 DKK

**Questions:**
a) What is the price for 1 Danish water, 1 roll with butter, and one optional cake?  
b) If the teacher eats the same thing 4 times a month, what will the total cost be for 52 weeks (a year)?

**Solution for a)**:
- Danish water: 15 DKK
- Roll with butter: 37 DKK
- Optional cake: 23 DKK

Total for a meal:  
\( 15 + 37 + 23 = 75 \) DKK

**Solution for b)**:  
4 times per month for a year (52 weeks, equivalent to 13 months):  
\( 75 \times 4 \times 13 = 3900 \) DKK

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### **Opgave 3** (Problem 3):
A class with 22 students and 2 teachers are going on a trip to Sæby for 5 days (4 nights). They will stay in cabins at a campsite. The costs per person are:
- Food: 65 DKK/day × 5 days
- Rental of the cabin: 85 DKK/night × 4 nights
- Excursions: 125 DKK
- Other costs: 2500 DKK total (shared among all participants)

**Questions:**
a) What is the total cost of the trip?  
b) What is the cost per participant (round to the nearest whole number)?

**Solution for a)**:  
- Food: \( 65 \times 5 = 325 \) DKK per person
- Cabin: \( 85 \times 4 = 340 \) DKK per person
- Excursions: 125 DKK per person
- Other shared costs: 2500 DKK total, shared by 24 people (22 students + 2 teachers), so:  
\( \frac{2500}{24} \approx 104.17 \) DKK per person

Total per person:  
\( 325 + 340 + 125 + 104.17 = 894.17 \) DKK

**Solution for b)**:  
Rounded to the nearest whole number: 894 DKK per participant.

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### **Opgave 4** (Problem 4):
Oliver’s parents offer him 6% interest per year if he leaves his confirmation money (25,000 DKK) in the bank.

**Questions:**
a) What will Oliver have after the first year?  
b) What will he have after 3 years?

**Solution for a)**:  
After the first year, his balance grows by 6%:  
\( 25000 \times 1.06 = 26500 \) DKK

**Solution for b)**:  
Using compound interest, after 3 years:  
\( 25000 \times (1.06)^3 \approx 29838 \) DKK

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Would you like to dive deeper into any of these solutions? Let me know if you have any questions!

Here are five related questions to explore further:
1. How would the total cost change if Peter bought an additional item in **Opgave 1**?
2. What if the teacher in **Opgave 2** adds ice cream to their order—how does that affect the yearly total?
3. If the trip in **Opgave 3** had lasted 6 days instead of 5, how much would each participant pay?
4. How much interest would Oliver earn after 5 years at the same rate in **Opgave 4**?
5. What if Oliver's interest rate was 5% instead of 6%? How would that affect his savings after 3 years?

### **Tip**: For compound interest, remember the formula \( A = P(1 + \frac{r}{n})^{nt} \), where:
- \( P \) is the principal amount (initial money),
- \( r \) is the annual interest rate,
- \( n \) is the number of times interest is compounded per year,
- \( t \) is the time in years.

Calculate total cost, savings, and interest rates.

Learn how to calculate total costs, change, and compound interest using basic arithmetic operations. This exercise is ideal for students in Grades 6-8 and covers fundamental concepts such as addition, subtraction, and percentage calculations.

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