Question

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If the following scenario is represented as a system of inequalities, which of the constraints is a part of the system?
Let z represent the number of hours my dad works and y represent the number of hours my mom works in a given week. My dad earns $21 dollars per hour at his job, and my
mom earns $23 dollars per hour at her job. The number of hours they work each week will vary, but my dad always works more hours than my mom, and all together, they eam at
least $2,000 each week but never work more than a total of 100 hours in a week.
Is
232.000

Answer 1

The system of inequalities for the scenario includes constraints such as z > y (dad works more hours than mom), 21z + 23y ≥ 2000 (combined earnings of at least $2,000), and z + y ≤ 100 (total work hours do not exceed 100 per week).

Step-by-step explanation:

The constraints for the given scenario can be expressed as a system of inequalities.

Let z represent the number of hours my dad works and y represent the number of hours my mom works in a given week.

Considering the information provided:

• My dad always works more hours than my mom, which can be written as: z > y.
• All together, they earn at least $2,000 each week, where dad earns $21 per hour and mom earns $23 per hour. The inequality representing their combined earnings is: 21z + 23y ≥ 2000.
• They never work more than a total of 100 hours in a week. This is represented by the inequality: z + y ≤ 100.

Therefore, the constraint that is part of the system is either z > y, 21z + 23y ≥ 2000, or z + y ≤ 100, depending on the specific question being asked about the constraints.