Answered

During a sleepover, Jayden played karaoke with her friends. Her song was 5 minutes long. She had already sung for 2 minutes. Which equation could be used to see how much longer she will have to sing?


A$x+2=5$
B$x+3=5$
C$x-2=5$
D$x+2=7$

Verified Answer :

  • The total duration of the song is \(5\) minutes, which is the sum of the time already sung (\(2\) minutes) and the time remaining (\(x\) minutes).
  • We express this relationship as the equation \(x + 2 = 5\).
  • Comparing this to the given options, the equation \(x + 2 = 5\) is the correct representation.
  • The correct option is \(\boxed{x + 2 = 5}\).

Explanation

  1. Analysis of the Song Duration Problem

To solve the problem, we need to determine the relationship between the total duration of the song, the time already sung, and the remaining time. We know that the total duration of the song is 5 minutes. Jayden has already sung for 2 minutes. Let \(x\) represent the number of minutes remaining in the song. The total time of the song is composed of the time she has already sung plus the time she has left to sing. Therefore, we can express this as the sum of these two parts: 2 minutes (already sung) + \(x\) minutes (remaining) = 5 minutes (total). This gives us the equation \(2 + x = 5\). Using the commutative property of addition, which states that \(a + b = b + a\), we can rewrite this as \(x + 2 = 5\).

  1. Selecting the Correct Equation

Now that we have established the equation \(x + 2 = 5\), we compare it to the options provided:

  • \(x + 2 = 5\): This matches our derived equation.
  • \(x + 3 = 5\): This represents a scenario where she had already sung for 3 minutes.
  • \(x - 2 = 5\): This would imply that the remaining time is 2 minutes more than the total time, which is incorrect.
  • \(x + 2 = 7\): This implies a total duration of 7 minutes.

Thus, the correct equation to determine the remaining time is \(x + 2 = 5\).

Examples

This type of problem helps in understanding how to set up simple algebraic equations from real-world situations. For instance, if you have a budget of \(\$50\) and you have already spent \(\$20\) on groceries, you can use the equation \(x + 20 = 50\) to calculate how much money, \(x\), you have remaining for other expenses. Recognizing these relationships is a fundamental skill in everyday budgeting and resource management.

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