Question

which scenario can be represented using the inequalities below?
$1.25 \leq x \leq 1.5$
a container of milk costs at least $1.25 but less than $1.50.
a student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework.
a tip added to a restaurant bill is less than or equal to 25% or less than or equal to 50%.
the point value of a test item is more than 1.25 points and less than 1.5 points.

Explanation:

1. Analyze the inequality $1.25 \leq x \leq 1.5$: this means $x$ is greater than or equal to 1.25, and less than or equal to 1.5.
2. Evaluate each option:

• Option 1: States "less than $1.50$", which would be $1.25 \leq x < 1.5$, not matching the given inequality.
• Option 2: Convert time to hours: 1 hour 15 minutes = 1.25 hours, 1 hour 30 minutes = 1.5 hours. The phrase "at least 1 hour 15 minutes, but no more than 1 hour 30 minutes" translates to $1.25 \leq x \leq 1.5$, which matches the inequality.
• Option 3: The description is logically unclear and does not map to the given range for a single variable $x$.
• Option 4: States "more than 1.25 points and less than 1.5 points", which would be $1.25 < x < 1.5$, not matching the given inequality.

Answer:

B. A student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework.