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The question in the image is in Swedish. Here's a translation to English:

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**2.** The price of a mobile phone first increases by 20%. The next month, the new price is decreased by 20%. Is the final price after both changes higher, lower, or the same compared to the original price? Provide a clear explanation for your reasoning.

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### Solution:
Let the original price of the mobile phone be \( P \).

1. **First increase of 20%:**
   The new price after a 20% increase is:
   \[
   P_{\text{new}} = P \times 1.20 = 1.20P
   \]

2. **Then a 20% decrease:**
   The price is now decreased by 20%, but it's a decrease on the new price (\( 1.20P \)), not the original price. So, the new price after the decrease is:
   \[
   P_{\text{final}} = 1.20P \times (1 - 0.20) = 1.20P \times 0.80 = 0.96P
   \]

   The final price is 96% of the original price, which means the price is **lower** than the original price.

### Conclusion:
After both changes, the final price is 96% of the original price, which is lower than the original price.

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Do you have any further questions or need more details? 

Here are some related questions you might find interesting:

1. What would happen if the price increased by 50% and then decreased by 50%?
2. How would you calculate the net percentage change in this case?
3. What if the price decreased first and then increased by the same percentage?
4. How can you express the final price as a percentage of the original price after multiple percentage changes?
5. How does the concept of compounding affect price changes like these?

**Tip:** When dealing with percentage changes, remember that increasing and then decreasing by the same percentage does not bring you back to the original value!

Priset på en mobiltelefon ökar först med 20 %. Månaden efter sänks det nya priset med 20 %. Är slutpriset efter de båda förändringarna högre, lägre eller desamma jämfört med det ursprungliga priset? Ge en tydlig förklaring till ditt resonemang.

Analyze the effect of a 20% price increase followed by a 20% price decrease on a mobile phone. Understand how percentage changes affect the final price, using algebraic concepts and formulas. Suitable for students in Grades 7-9.

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