At Annville Junior High School, $30\%$ of the students in the Math Club are in the Science Club, and $80\%$ of the students in the Science Club are in the Math Club. There are 15 students in the Science Club. How many students are in the Math Club?
I need to find the number of students in the Math Club, so I will call that x. Since $30\%$ of the students in the Math Club are in the Science Club, that means $0.3x$ students are in both clubs. Since $80\%$ of the students in the Science Club are in the Math Club, that means $0.8 \times 15 = 12$ students are in both clubs. Therefore, I can set up an equation to equate the two expressions for the number of students in both clubs: $0.3x = 12$. To solve for x, I can divide both sides by 0.3: $x = 12 / 0.3 = 40$. So there are 40 students in the Math Club. 