Jenna works at a factory where she makes boxes for shipping food products. She earns $3 per hour plus $0.41 for every box she makes. If n is the number of boxes that Jenna makes in 2 hours, her earnings in dollars for the 2 hours are given by:

Question

Jenna works at a factory where she makes boxes for shipping food products.  She earns $3 per hour plus $0.41 for every box she makes.  If n is the number of boxes that Jenna makes in 2 hours, her earnings in dollars for the 2 hours are given by:

BlackTom AI · Accepted Answer

Jenna’s earnings come from two parts: a fixed hourly wage over the two hours, and a per-box payment based on how many boxes she makes in that period.
To compute the total, multiply the hourly rate by the total hours (3 dollars per hour × 2 hours = 6 dollars) and add the per-box earnings (0.41 dollars per box × n boxes).
Now evaluate each option:

Option 1: 3 + 0.82n
This expression uses 3 as the base, which would correspond to 1 hour of work at $3 per hour, not 2 hours. Additionally, it uses 0.82n for the per-box term, which doubles the given per-box rate (0.41 × 2 = 0.82). Both parts are incorrect for the described scenario.

Option 2: 6 + 0.41n
This matches the reasoning: 6 dollars for the two hours of work (3 × 2) plus 0.41 dollars for each of the n boxes. It aligns with the statement of earnings being $3 per hour plus $0.41 per box over two hours.

Option 3: 3 + 0.41n
Here, the hourly portion is only 3 dollars, which would imply earnings for only 1 hour, not 2. The per-box portion 0.41n is correct in form, but the fixed-hour component is incorrect for the two-hour time frame.

Option 4: 3.41n
This expression treats earnings as entirely dependent on the number of boxes, with a coefficient of 3.41 per box, effectively ignoring the fixed 2-hour salary and misallocating the per-box rate. It does not reflect the two-part structure described.

Option 5: 6 + 0.82n
The 6 part correctly accounts for 2 hours at $3 per hour, but the per-box term uses 0.82n, which equals 0.41 × 2, doubling the stated per-box rate. This overcounts the box earnings.

In summary, each option deviates from the described pay structure in different ways: some miscount the hours, some misapply the per-box rate, and others combine both errors in various forms. Paying attention to both components—the fixed 2-hour pay and the per-box pay—helps distinguish the correct formulation from the incorrect ones.

MATH 1151 AU2025 (18443) Calculus Concept Readiness Assessment (CCR)

Jenna works at a factory where she makes boxes for shipping food products. She earns $3 per hour plus $0.41 for every box she makes. If n is the number of boxes that Jenna makes in 2 hours, her earnings in dollars for the 2 hours are given by:

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