A chess team has $26$ members. However, only $16$ members attended the last meeting: half of the girls attended but all of the boys attended. How many girls are on the chess team?
To solve this problem, I need to find a way to relate the total number of members, the number of attendees, and the fractions of girls and boys. I can start by using a variable to represent the number of girls on the team. Let me call it $g$. Then, the number of boys on the team must be $26 - g$, since the total is $26$. Now, I can write an equation for the number of attendees, using the information given in the problem. The problem says that half of the girls attended, so that means $\frac{1}{2}g$ girls attended. The problem also says that all of the boys attended, so that means $26 - g$ boys attended. Adding these two terms, I get the total number of attendees, which is $16$. So, my equation is: $\frac{1}{2}g + 26 - g = 16$. I can simplify this equation by combining like terms. I get: $-\frac{1}{2}g + 26 = 16$. Then, I can subtract $26$ from both sides. I get: $-\frac{1}{2}g = -10$. To solve for $g$, I can multiply both sides by $-2$. I get: $g = 20$. This means that there are $20$ girls on the chess team. 