Which scenario can be represented using the inequalities below?
[tex]$1.25 \leq x \leq 1.5$[/tex]
A. A container of milk costs at least $1.25 but less than $1.50.
B. A student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework.
C. A tip added to a restaurant bill is less than or equal to 25% or less than or equal to 50%.
D. The point value of a test item is more than 1.25 points and less than 1.5 points.
Answer (2)
Scenario 1 matches the inequality 1.25 ≤ x ≤ 1.5 .
Scenario 2 also matches the inequality 1.25 ≤ x ≤ 1.5 .
Scenario 3 does not fit the inequality.
Scenario 4 does not match the inequality because it doesn't include the endpoints.
Scenarios 1 and 2 are correct. Since scenario 1 is listed first, we choose that one. The final answer is A.
Explanation
Analyzing the Problem We are given the inequality 1.25 ≤ x ≤ 1.5 and four scenarios. We need to determine which scenario can be represented by the given inequality. Let's analyze each scenario.
Checking Scenario 1 Scenario 1: A container of milk costs at least $1.25 but less than or equal to $1.50 . This can be written as 1.25 ≤ x ≤ 1.5 . This matches the given inequality.
Checking Scenario 2 Scenario 2: A student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework. 1 hour 15 minutes is equal to 1.25 hours, and 1 hour 30 minutes is equal to 1.5 hours. So, this can be written as 1.25 ≤ x ≤ 1.5 . This also matches the given inequality.
Checking Scenario 3 Scenario 3: A tip added to a restaurant bill is less than or equal to 25% or less than or equal to 50% . This does not fit the inequality 1.25 ≤ x ≤ 1.5 because it represents percentages, not a range between 1.25 and 1.5.
Checking Scenario 4 Scenario 4: The point value of a test item is more than 1.25 points and less than 1.5 points. This can be written as 1.25 < x < 1.5 . This does not match the given inequality because it does not include the endpoints 1.25 and 1.5.
Final Answer Since both Scenario 1 and Scenario 2 match the inequality 1.25 ≤ x ≤ 1.5 , we need to choose the best answer. The question does not specify that only one answer is correct. However, since the first option is listed first, we will choose that one.
Examples
Understanding inequalities like 1.25 ≤ x ≤ 1.5 helps in everyday scenarios such as budgeting. For instance, if you're planning your daily coffee expenses, knowing that you'll spend between $1.25 and $1.50 each day allows you to manage your finances effectively. This concept extends to various financial planning situations, from tracking grocery costs to setting savings goals, ensuring you stay within your desired spending limits.
The scenario that fits the inequality 1.25 ≤ x ≤ 1.5 is A: A container of milk costs at least $1.25 but less than $1.50. Scenario B also matches the inequality, but A is chosen as it appears first. Therefore, the selected answer is A.
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