Describe a real world scenario that could be modeled by the following inequality. You should also define what the variable, x, is representing based on your example.
7x+10≥85
A real-world scenario that could be modeled by the inequality 7x + 10 ≥ 85 is a person's monthly income and expenses.
In this case, the variable x represents the amount of money the person earns per month. The inequality states that the person's monthly income multiplied by 7 (indicating seven times a week) and added to 10 (representing their remaining expenses) should be greater than or equal to 85 (their target amount to save or meet their financial goals).
For example, let's assume the person's monthly income is $10. Plugging this value into the inequality, we get:
7(10) + 10 ≥ 85
70 + 10 ≥ 85
80 ≥ 85
Since 80 is not greater than or equal to 85, this person with a monthly income of $10 would not achieve their financial goals or have enough money left over after expenses.
A real-world scenario that could be modeled by the inequality 7x + 10 ≥ 85 is the situation of a student's grades in a class. In this scenario, the variable x represents the number of assignments a student has completed, and the inequality represents the minimum score the student needs to achieve on their assignments in order to pass the class.
For example, let's say a student has completed x assignments, and for each assignment, they can earn a maximum of 100 points. The inequality suggests that the sum of the points they have earned, multiplied by 7 and added to 10, should be greater than or equal to 85, which is the minimum passing score.
To determine if the student will pass the class, we can substitute different values for x into the inequality. For instance, if the student only completed one assignment (x = 1), the inequality becomes 7(1) + 10 ≥ 85, which simplifies to 7 + 10 ≥ 85, or 17 ≥ 85. Since 17 is not greater than or equal to 85, the student would not pass the class with just one assignment completed.
Similarly, if the student completed 11 assignments (x = 11), the inequality becomes 7(11) + 10 ≥ 85, which simplifies to 77 + 10 ≥ 85, or 87 ≥ 85. In this case, 87 is indeed greater than or equal to 85, so the student would pass the class with 11 assignments completed.