Video: Determining the System of Inequalities That Describes a Given Situation

A teacher gave his students 100 minutes to solve a test. The students had to solve at least 4 questions in section A, at least 6 questions from section B, and answer at least 11 questions in total. If a girl answered each question in section A in 3 minutes and each question in section B in 6 minutes, derive the system of inequalities that would help to know how many questions she tried to solve in each section.

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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.

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