To solve the questions, we use the formula for percentage calculations:

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(a) What percentage of $45 is $135?

The formula to find the percentage is: $\text{Percentage} = \left( \frac{\text{New Value}}{\text{Original Value}} \right) \times 100$

Here:

• New Value = $135
• Original Value = $45

Substitute into the formula: $\text{Percentage} = \left( \frac{135}{45} \right) \times 100 = 3 \times 100 = 300\%$

Thus, $135 is 300%$ of $45.

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(b) What is the percentage increase?

The formula for percentage increase is: $\text{Percentage Increase} = \left( \frac{\text{Increase in Value}}{\text{Original Value}} \right) \times 100$

Here:

• Increase in Value = New Value - Original Value = $135 - 45 = 90$
• Original Value = $45

Substitute into the formula: $\text{Percentage Increase} = \left( \frac{90}{45} \right) \times 100 = 2 \times 100 = 200\%$

Thus, the percentage increase is $200\%$.

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Final Answers:

1. $135$ is 300% of $45$.
2. The percentage increase is 200%.

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Would you like a detailed step-by-step breakdown of these calculations?

Here are 5 related questions to explore:

1. How do you calculate the percentage decrease if the price goes back to $45?
2. If the price increased to $180 instead, what would the new percentage increase be?
3. What is the formula for calculating percentage change in general?
4. How do percentage increase and percentage of a value differ conceptually?
5. How can you calculate the original price if only the percentage increase and the final price are known?

Tip: Always double-check whether a question asks for "percentage of a value" or "percentage change" as they involve different calculations!