There are x students in the journalism club. There are 7 fewer students in the art club than in the journalism club, and there are 25% more students in the chess club than the art club for a total of 15 students in the chess club. How many students are in the journalism club?

Choose the tape diagram that represents the number of students in the art club.

x
journalism

art
7
x

x
journalism

art
x −7
Good work!
Choose the tape diagram that represents the number of students in the chess club.

x
journalism

art
x −7
chess
15

x
journalism

art
x −7
chess
15
You got it!
Write an equation in words to represent this situation.
x
journalism

art
x −7
chess
15

125% of art club = chess club

150% of art club = chess club

50% of art club = chess club

25% of art club = chess club
Great job!
Write an equation to represent this situation.
x
journalism

art
x −7
chess
15
125% of art club = chess club
Great job!
Solve the equation to find the value of x. You can show your work on Zearn or on paper, then enter your answer on Zearn.
1.25(x−7)
=
15

x
=
Nice!
What does x = 19 represent in this situation?

There are 19% fewer students in the art club than the chess club.

There are 19 students in the journalism club.

There are 19 students in the art club.

1 answer

To clarify the situation step-by-step, let’s follow through with the information given:

  1. Let \( x \) be the number of students in the journalism club.
  2. The number of students in the art club is \( x - 7 \) (7 fewer than the journalism club).
  3. The chess club has 25% more students than the art club. Since there are 15 students in the chess club, we can translate this into an equation.

We want to say that 125% (100% + 25%) of the art club is equal to the chess club. So, if the number of students in the art club is \( x - 7 \), we write:

\[ 1.25 \times (x - 7) = 15 \]

Now, let's solve for \( x \):

  1. Start with the equation: \[ 1.25(x - 7) = 15 \]

  2. Distributing \( 1.25 \): \[ 1.25x - 8.75 = 15 \]

  3. Add \( 8.75 \) to both sides: \[ 1.25x = 15 + 8.75 \] \[ 1.25x = 23.75 \]

  4. Divide both sides by \( 1.25 \): \[ x = \frac{23.75}{1.25} = 19 \]

Thus, \( x = 19 \).

Now, interpreting \( x = 19 \) in this situation:

What does \( x = 19 \) represent?

It means:

  • There are 19 students in the journalism club.

So the correct answer is:

There are 19 students in the journalism club.