Look at another example.

Question

Jessica and Jaime eat out at a restaurant. The bill comes to n dollars, and they leave a 22% tip for their server. There are two ways Jessica and Jaime can write an expression to represent their total cost.

The first way is to write the base cost and the tip as two separate parts. In this example, the base cost is n . The tip is 22% of n . Because 22% is equal to 0.22, the amount of the tip can be written as 0.22n . To find the total, write an expression that adds these two separate amounts: In all, Jessica and Jaime spend n + 0.22n dollars.

Before you read ahead, think of what you know about mathematical structure. Is there a way to combine these two terms according to the rules of mathematical operations?

The second way is to combine the two terms above into a single term.

Because n = 1n , n + 0.22n can be thought of as 1.22n .

Which expression is correct? Again, the answer is both. The first way has the advantage of breaking down the amounts to make it clearer how much money Jessica and Jaime are spending on the meal compared to how much they are spending on the tip.

The second focuses more specifically on the total cost without looking at the breakdown. Looking at the problem from both perspectives helps you see the relationship between them and deepens your understanding of what the problem is all about.

Answer 1

Both expressions are correct. They represent the same value and can be used interchangeably. The first expression breaks down the base cost and tip separately, while the second expression combines them into a single term. Both expressions provide different perspectives on the problem and contribute to a deeper understanding of the relationship between the base cost and the tip.