An archery target has 3 regions, each worth a different value if it is hit. Three archers shoot two arrows each and record scores as follows:

First archer: 1 arrow in $C$ and 1 arrow in $A$ for a score of 15 points Second archer: 1 arrow in $C$ and 1 arrow in $B$ for a score of 18 points Third archer: 1 arrow in $B$ and 1 arrow in $A$ for a score of 13 points

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-118.jpg?height=340&width=354&top_left_y=1872&top_left_x=1402)

If a fourth archer shoots 2 arrows into ring $B$, her score is
(A) 10
(B) 14
(C) 16
(D) 18
(E) 20

## Part C: Each correct answer is worth 8.
Let $a$ be the value of an arrow shot into ring $A$, let $b$ be the value of an arrow shot into ring $B$, and let $c$ be the value of an arrow shot into ring $C$.

From the given information about the three archers, we know that

$$
\begin{aligned}
& c+a=15 \\
& c+b=18 \\
& b+a=13
\end{aligned}
$$

We are interested in calculating $2 b$.

Adding up the second and third equations, we get $a+2 b+c=31$ and so substituting the information from the first equation, we get $2 b+15=31$ or $2 b=16$.

(Notice that we could have found the values of $a, b$ and $c$, but we did not need to do this.)