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Annette’s soccer team will play 15 games this season that is seven games fewer than two times the number of games they play last season how many games did they play last season represent this problem with an equation in the form px + q = r. pls

3 answers

To represent the problem with an equation in the form \( px + q = r \), we need to define a variable for the number of games played last season.

Let \( x \) be the number of games Annette's soccer team played last season.

According to the problem, we know that:

  1. This season, they will play 15 games.
  2. The number of games played this season (15) is seven games fewer than two times the number of games played last season (2x).

We can express this relationship as:

\[ 15 = 2x - 7 \]

To rewrite this equation in the form \( px + q = r \), we can rearrange it:

  1. Start with \( 15 = 2x - 7 \).
  2. Add 7 to both sides:

\[ 15 + 7 = 2x \]

This simplifies to:

\[ 22 = 2x \]

This leads us to the equation:

\[ 2x - 22 = 0 \]

Therefore, in the form \( px + q = r \):

  • \( p = 2 \)
  • \( q = -22 \)
  • \( r = 0 \)

So the equation is:

\[ 2x - 22 = 0 \]

are u sure

Let's go through the problem step by step to ensure accuracy.

  1. We need to find the number of games played last season, which we'll denote as \( x \).

  2. According to the problem:

    • This season, Annette's team will play 15 games.
    • This is stated to be seven games fewer than two times the number of games played last season.

From the information provided, we can set up the equation as follows:

\[ 15 = 2x - 7 \]

Next, let's rearrange the equation to get it into the form \( px + q = r \):

  1. Add 7 to both sides of the equation:

\[ 15 + 7 = 2x \]

This simplifies to:

\[ 22 = 2x \]

  1. Now, rearranging it into the standard form:

\[ 2x - 22 = 0 \]

In this case:

  • \( p = 2 \)
  • \( q = -22 \)
  • \( r = 0 \)

So the equation \( 2x - 22 = 0 \) is indeed correct.

To verify, let's solve for \( x \):

\[ 2x = 22 \]

\[ x = 11 \]

So, Annette's soccer team played 11 games last season.

Final verification:

  • Two times the number of games last season: \( 2 \times 11 = 22 \)
  • Seven games fewer than that: \( 22 - 7 = 15 \)

This matches with the provided information about the number of games played this season.

Therefore, the equation \( 2x - 22 = 0 \) is correct, and the solution for the number of games played last season is \( x = 11 \).