### Video Transcript

A teacher gave his students 100
minutes to solve a test. The students had to solve at least
four questions in section A, at least six questions from section B, and answer at
least 11 questions in total. If a girl answered each question in
section A in three minutes and each question in section B in six minutes, derive the
system of inequalities that would help to know how many questions she tried to solve
in each section.

We will use the letter 𝑥 to
represent the number of questions answered from section A and the letter 𝑦 to
represent the number of questions answered from section B.

Let’s now pick out the key
information. The total time for the test was 100
minutes. The girl answered a question in
section A, letter 𝑥, in three minutes and a question in section B in six
minutes.

We also know that she had to answer
at least four questions from section A, at least six questions from section B, and
at least 11 questions in total.

As it took her three minutes to
answer a question in section A, three multiplied by 𝑥 gives us three 𝑥, the total
time to answer questions from section A. In a similar way, it took her six
minutes to answer a question from section B. Six multiplied by 𝑦 is six 𝑦.

When we add these together, the
time she spent on section A plus the time she spent on section B, we know that this
answer must be less than or equal to 100 minutes as this was the total time.

Therefore, our first inequality is
three 𝑥 plus six 𝑦 less than or equal to 100. As the number of questions answered
in section A was denoted by the letter 𝑥, and this needed to be at least four, we
can say that 𝑥 is greater than or equal to or bigger than or equal to four.

In the same way she needed to
answer at least six questions from section B. So 𝑦 is bigger than or equal to,
more than or equal to, six. And finally, the total number of
questions needed to be at least 11.

Therefore, the number of questions
in section A, 𝑥, plus the number of questions in section B, 𝑦 must be bigger than
or equal to or more than or equal to 11.

This leaves us with a system of
four inequalities that would help to know how many questions she tried to solve in
each section.