Question

Reid and Maria both play soccer. This season, Reid scored 4 less than twice the number of goals that Maria scored. The difference in the number of goals they scored was 6. How many goals did each of them score?

Answer 1

Let \(R\) and \(M\) denote the number of goals Reid and Maria scored, respectively. Then
\[\begin{cases}
R=2M-4\\
|R-M|=6
\end{cases}\]
The second equation says either \(R-M=6\) or \(M-R=6\); we're not sure yet whether \(M\) or \(R\) is greater.

Suppose it's \(R-M=6\), then \(R=M+6\) and subbing into the first equation of the system gives
\[M+6=2M-4~~\iff~~M=10~~\Rightarrow~~R=16\]
Suppose it's \(M-R=6\), then \(M=R+6\) and
\[R=2(R+6)-4~~\iff~~\color{red}{R=-12}~~\Rightarrow~~\color{red}{M=-6}\]
Clearly the first case must be true, since you can't score negative goals.