In a quiz game, a player earns 5 points for every correct answer and loses 3 point for every wrong answer. If Steve’s score is 0 after answering 40 questions, how many questions did he answer correctly?
My approach isn't very mathematical, I'm sure there is a better approach but here's mine. Some mathematical principle but most trial and error.
You want to find a common multiple. If Steve's score is $\displaystyle 0$, then this meant that he lost on more occasion that won.
The common multiple of $\displaystyle 3$ and $\displaystyle 5$ are:
$\displaystyle 15, 30, 45, 60, 75, 90 $ etc.
At which value would the alternative pair add upto $\displaystyle 40$. This would be $\displaystyle 75$ because:
$\displaystyle 75 \div 3 = 25$
$\displaystyle 75 \div 5 = 15$
The alternative pair $\displaystyle 25$ and $\displaystyle 15$ add to make $\displaystyle 40$.
This means, Steve lost $\displaystyle 25$ times and won $\displaystyle 15$ times.