The problem in the image involves finding the total percentage increase and the new price of a calculator that originally costs 150 dollars, with two successive percentage increases of 10% and 20%.

To solve this, you are given the formula for calculating the combined increase from two consecutive percentage increases:

$Au = \left( A_1 + A_2 + \frac{A_1 \times A_2}{100} \right) \%$

Where:

• $A_1 = 10\%$ (first increase),
• $A_2 = 20\%$ (second increase).

Step 1: Calculate the total percentage increase

$Au = \left( 10 + 20 + \frac{10 \times 20}{100} \right) \%$

$Au = (10 + 20 + 2) = 32\%$

So, the total increase is 32%.

Step 2: Calculate the new price of the calculator

Now, we apply the 32% increase to the original price of 150 dollars:

$\text{New Price} = 150 + 150 \times \frac{32}{100}$

$\text{New Price} = 150 + 48 = 198 \text{ dollars}$

Final Answer:

• Total Increase: 32%
• New Price: 198 dollars.

Would you like further details or have any questions?

Here are 5 related questions you might find interesting:

1. How do you calculate the overall percentage increase if there are three successive increases?
2. What would happen if one of the percentage changes was a decrease instead of an increase?
3. How does compound interest relate to successive percentage increases?
4. Can we use the same formula for decreases in percentages, and how?
5. What would be the final price if both increases were 50%?

Tip: When dealing with successive percentage changes, multiplying the individual changes often leads to a higher final change than simply adding them!