Question

there are x students in the robotics club. there are 7 more students in the art club than in the robotics club, and there are 50% more students in the chess club than the art club for a total of 30 students in the chess club. how many students are in the robotics club? robotics x art 7 x chess 30 50% of art club = chess club 125% of art club = chess club 25% of art club = chess club 150% of art club = chess club

Explanation:

Step1: Determine the correct percentage relation

The chess club has 50% more students than the art club. 50% more means the chess club has \(100\% + 50\%=150\%\) of the art club's students. So the correct relation is \(150\%\) of art club = chess club.

Step2: Find the number of students in the art club

Let the number of students in the art club be \(y\). We know that \(150\%\) of \(y\) is 30 (since chess club has 30 students). Converting \(150\%\) to a decimal, we get \(1.5\). So the equation is \(1.5y = 30\). Solving for \(y\), we divide both sides by \(1.5\): \(y=\frac{30}{1.5}=20\).

Step3: Find the number of students in the robotics club

The art club has 7 more students than the robotics club. Let the number of students in the robotics club be \(x\). Then the number of students in the art club \(y=x + 7\). We found \(y = 20\), so \(x+7=20\). Subtracting 7 from both sides, we get \(x=20 - 7 = 13\).

Answer:

The number of students in the robotics club is \(\boldsymbol{13}\).