1. ## word problem

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?

2. Originally Posted by amywright00
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.

3. Originally Posted by amywright00
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?
Here is one way.

Let x = number of correct answers
So, (40 -x) = number of wrong answers.

(x)(5) -(40 -x)(3) = o
5x -120 +3x = 0
8x = 120
x = 120/8 = 15 correct answers
So,
(40 -x) = (40 -15) = 25 wrong answers.