In a quiz a team is given 5 points for every correct answer and loses 2 points for every wrong one. The team attempted 25 questions and finished with 90 points. How many questions did it answer correctly?

Let $c$ questions be right and $w$ wrong. $c+w=25$ and $5c-2w=90$. Substituting $w=25-c:5c-50+2c=90$, so $7c=140$ and $c=20$, giving $w=5$. Check: 20 + 5 = 25 and 100 - 10 = 90. 5 is the number of wrong answers; 18 comes from 90 divided by 5, which ignores the points lost on wrong answers; 25 is simply the number attempted.