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?
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.