Which algebraic expression represents "Marcus practiced the trumpet twice as long this week"?
To represent the phrase "Marcus practiced the trumpet twice as long this week" algebraically, we first define our variable. Let \(p\) represent the amount of time Marcus practiced the trumpet in a reference period (or this week).
The phrase "twice as long" describes a quantitative relationship. In mathematics, the word "twice" signifies multiplication by the factor \(2\). Therefore, "twice as long" as the time \(p\) is calculated by multiplying \(p\) by \(2\), which is written as \(2p\).
We are given four options to choose from:
Comparing these with our derived expression, we see that \(2p\) is the correct representation.
Based on our analysis, the correct algebraic expression for "Marcus practiced the trumpet twice as long this week" is \(2p\). Therefore, the correct option is the second one. The final answer is \(\boxed{2p}\).
Understanding how to translate word problems into algebraic expressions is a foundational skill in algebra. For instance, if you know the price of a movie ticket is \(t\), and you want to calculate the cost for two people, you can express it as \(2t\). Recognizing these patterns helps you model real-world situations, such as budgeting, scaling recipes, or calculating distances, using simple mathematical language.