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

Shady and Fares went on a tour driving to Luxor and Aswan and took turns driving; each day Shady drove for at least 4 hours and NO more than 8 hours, while Fares drove at least 2 hours and less than 7 hours. The total time they drove daily was NO more than 9 hours. State the system of inequalities that describes the situation, using 𝑥 to represent the number of hours Shady drove and 𝑦 to represent the number of hours Fares drove.

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Video Transcript

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

As Shady drove for at least four hours and no more than eight hours, we can say that 𝑥 is greater than or equal to four and also less than or equal to eight. Or 𝑥 lies between four and eight.

Fares on the other hand drove for at least two hours and less than seven hours. This means that 𝑦 is greater than or equal to two, but less than seven.

Our final inequality comes from the total time. The total time that they drove was no more than nine hours. Therefore, 𝑥 plus 𝑦 must be less than or equal to nine. This leaves us with a system of three inequalities that describe the situation.

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 nine.

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