Value of the tokens

Statement

In a board game each red token is worth $r$ points and each blue token is worth $b$ points. Two red tokens and one blue token are worth $8$ points altogether; one red token and two blue tokens are worth $7$ points. How much is a red token worth?

Solution

System. Translate the two conditions: $\begin{cases} 2r + b = 8\\ r + 2b = 7 \end{cases}$ From the first, $b = 8 - 2r$; substitute into the second: $r + 2(8 - 2r) = 7 \implies r + 16 - 4r = 7 \implies -3r = -9 \implies r = 3.$ Then $b = 8 - 2\cdot 3 = 2$. Check: $2\cdot 3 + 2 = 8$ and $3 + 2\cdot 2 = 7$. Correct. $\boxed{r = 3 \text{ points}, \quad b = 2 \text{ points}}$