# Question Video: Stating the System of Inequalities That Describes a Given Situation Mathematics • 9th Grade

Anthony and Daniel went on a driving tour to Luxor and Aswan and took turns driving. Each day, Anthony drove for at least 4 hours and no more than 8 hours, while Daniel drove at least 2 hours and less than 7 hours. The total time they drove daily was no more than 12 hours. State the system of inequalities that describes the situation using 𝑥 to represent the number of hours that Anthony drove and 𝑦 to represent the number of hours that Daniel drove.

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### Video Transcript

Anthony and Daniel went on a driving tour to Luxor and Aswan and took turns driving. Each day, Anthony drove for at least four hours and no more than eight hours, while Daniel drove at least two hours and less than seven hours. The total time they drove daily was no more than 12 hours. State the system of inequalities that describes the situation using 𝑥 to represent the number of hours that Anthony drove and 𝑦 to represent the number of hours that Daniel drove.

In this question, we are told to let 𝑥 represent the number of hours that Anthony drove and 𝑦 represent the numbers that Daniel drove. We are given information about both drivers together with the total time they drove. Let’s begin by considering Anthony, we are told that he drove for at least four hours and no more than eight hours each day. This means that 𝑥 must be greater than or equal to four and less than or equal to eight.

We are told that Daniel drove at least two hours and less than seven hours. This means that 𝑦 must be greater than or equal to two and less than seven. It is important to note that we have a strict inequality at the upper end, as Daniel drove less than seven hours. Finally, we are told that the total time they drove daily was no more than 12 hours. This total time will be the sum of 𝑥 and 𝑦. And we therefore have the inequality 𝑥 plus 𝑦 is less than or equal to 12.

The system of inequalities that describes the situation is 𝑥 is greater than or equal to four and less than or equal to eight, 𝑦 is greater than or equal to two and less than seven, and 𝑥 plus 𝑦 is less than or equal to 12. Whilst it is not required in this question, we could also model the situation graphically.