# how many questions did the answer in each round?

yolanda went on a quiz show. the question in the first round were worth 6 points. the questions in second round were worth 10 points. yolanda answered a total of 5 questions and earned 34 points. how many questions did the answer in each round?

• How hard can this be? If she answered 5 questions, that's 5 in the first round and none in the second, or 4 in the 1st and 1 in the 2nd, or.... Just check out all the possibilities --- there aren't that many. – Gerry Myerson Jun 13 '14 at 7:26
• Algebra is tricky to those who don't have 104k on Math Stack Exchange... @GerryMyerson – user124862 Jun 13 '14 at 7:29
• @Mitch, Algebra is not relevant to my comment, which showed how to solve the problem using nothing more advanced than addition of 2-digit numbers. – Gerry Myerson Jun 14 '14 at 5:24

Let $x$ be the number of questions answered in the first round, and $y$ be the number of questions in the second round. Now, she answered $5$ questions, thus $$x+y=5.$$ Also, she had a total of $34$ points, thus $$6x+10y=34.$$ We include the second equation based on the points for each question. Solving the first equation: $$x=5-y,$$ and substituting it into the second: $$6(5-y)+10y=34$$ $$\Longrightarrow 30-6y+10y=34 \Longrightarrow y=1.$$ Putting this value into the first equation yields $x=4$. Thus, she answered $4$ in the first round and $1$ in the second round.