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 boys are on the chess team?
Let there be $B$ boys and $G$ girls. Since every member is either a boy or a girl, $B+G=26$. Also, we have $\frac{1}{2}G+B=16$. Multiplying the second equation by $2$, we get $G+2B=32$. Subtracting the first equation from this, we get $B=32-26=6$.

Thus there are $\boxed{6}$ boys on the chess team.
6
Level 1
Algebra
Problem: 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 boys are on the chess team?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the number of boys on the chess team, we start with the total number of members, which is 26. We know that 16 members attended the last meeting. 

Let the number of boys be denoted as B and the number of girls as G. The relationship between boys and girls can be expressed as:
B + G = 26.

From the problem, we know that all boys attended the meeting, so the number of boys who attended is B. Half of the girls attended, which means the number of girls who attended is G/2. 

The total number of attendees can be expressed as:
B + (G/2) = 16.

Now we have a system of two equations:
1. B + G = 26
2. B + (G/2) = 16.

We can solve this system step by step. First, we can express G in terms of B using the first equation:
G = 26 - B.

Next, we substitute this expression for G into the second equation:
B + ((26 - B)/2) = 16.

To eliminate the fraction, we can multiply the entire equation by 2:
2B + (26 - B) = 32.

This simplifies to:
2B + 26 - B = 32,
which further simplifies to:
B + 26 = 32.

Now, we isolate B:
B = 32 - 26,
B = 6.

Thus, the number of boys on the chess team is 6.<|END_OF_LATENT|> The final answer is $6$.