Question

determining a reasonable solution set

pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level.

\\7h - 5(3h - 8) = -72\\

which statement is true about pieters solution?

• it cannot be a fraction or decimal because the depth of the well is a whole number.
• it must be a positive number since it represents a number of hours.
• it must be a negative number because the depth is below sea level.
• it cannot be greater than -72 because that is the depth of the well.

Explanation:

Identify the variable and context

The variable \(h\) represents the number of hours spent digging.
Time elapsed must be a non-negative quantity in real-world contexts.

Analyze the physical constraints

Since \(h\) represents a duration of time, it must be positive.
A negative number of hours is physically impossible for this scenario.

Evaluate the given options

• Option 1: Time can be fractional (e.g., half an hour).
• Option 2: Time must be positive, which is correct.
• Option 3: Time cannot be negative.
• Option 4: Comparing time \(h\) directly to depth \(-72\) is conceptually incorrect.

Select the correct statement

The statement "It must be a positive number since it represents a number of hours" is true.

Answer:

• (A) It cannot be a fraction or decimal because the depth of the well is a whole number.
• (B) It must be a positive number since it represents a number of hours. (Correct answer)
• (C) It must be a negative number because the depth is below sea level.
• (D) It cannot be greater than \(-72\) because that is the depth of the well.