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?

  • $\begingroup$ 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. $\endgroup$ – Gerry Myerson Jun 13 '14 at 7:26
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    $\begingroup$ Algebra is tricky to those who don't have 104k on Math Stack Exchange... @GerryMyerson $\endgroup$ – user124862 Jun 13 '14 at 7:29
  • $\begingroup$ @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. $\endgroup$ – 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.

  • $\begingroup$ This is useful, especially as an approach to handle more complicated problems. (+1) $\endgroup$ – robjohn Jun 13 '14 at 13:13

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