Andy, Beth, Charlie, and Daniel take a test with thirty questions. Andy and Beth together get the same number of questions wrong as Charlie and Daniel together. Andy and Daniel together get four more questions wrong than Beth and Charlie do together. If Charlie gets five questions wrong, how many questions does Andy get wrong?
Let $a$ denote the number of questions Andy got wrong, $b$ the number of questions Beth missed, $c$ the number of questions Charlie answered incorrectly, and $d$ the number of questions Daniel got wrong. Using the information given in the problem, we can form the following system of linear equations:  \begin{align*}
a + b &= c + d \\
a + d &= b+c +4 \\
c = 5
\end{align*} Adding the first two equations together yields $2a + b + d = 2c + b + d + 4$, which simplifies to $a = c + 2$. Since $c = 5$, Andy must have answered $\boxed{7}$ questions incorrectly.
7
Level 4
Algebra
Problem: Andy, Beth, Charlie, and Daniel take a test with thirty questions. Andy and Beth together get the same number of questions wrong as Charlie and Daniel together. Andy and Daniel together get four more questions wrong than Beth and Charlie do together. If Charlie gets five questions wrong, how many questions does Andy get wrong?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>Let A, B, C, and D represent the number of questions wrong for Andy, Beth, Charlie, and Daniel, respectively. 

From the problem, we have the following equations based on the information given:

1. A + B = C + D (Andy and Beth together get the same number wrong as Charlie and Daniel together).
2. A + D = B + C + 4 (Andy and Daniel together get four more wrong than Beth and Charlie together).
3. C = 5 (Charlie gets five questions wrong).

Substituting C = 5 into the first equation gives us:

A + B = 5 + D.

Substituting C = 5 into the second equation gives us:

A + D = B + 5 + 4, which simplifies to A + D = B + 9.

Now we have two equations:

1. A + B = 5 + D.
2. A + D = B + 9.

We can express B from the first equation:

B = 5 + D - A.

Substituting this expression for B into the second equation:

A + D = (5 + D - A) + 9.

Simplifying this gives:

A + D = 5 + D - A + 9,
A + D = D + 14 - A.

Rearranging terms leads to:

2A = 14,
A = 7.

Thus, Andy gets 7 questions wrong. The final answer is 7.<|END_OF_LATENT|> The final answer is $7$.