A team of workers has been moving cargo off of a ship. The equation below models the approximate number of...

1. TRANSLATE the problem information

• Given equation: \(\mathrm{y = 120 - 25x}\)
• Where: y = tons of cargo remaining, x = hours after starting
• Need to find: interpretation of x-intercept

2. INFER what finding the x-intercept means

• X-intercept occurs where the graph crosses the x-axis
• This happens when \(\mathrm{y = 0}\)
• In context: when \(\mathrm{y = 0}\), there are 0 tons of cargo remaining

3. SIMPLIFY to find the x-intercept

• Set \(\mathrm{y = 0}\): \(\mathrm{0 = 120 - 25x}\)
• Add 25x to both sides: \(\mathrm{25x = 120}\)
• Divide by 25: \(\mathrm{x = 4.8}\)

4. TRANSLATE the mathematical result back to context

• When \(\mathrm{x = 4.8}\) hours, \(\mathrm{y = 0}\) tons remain
• This means: after 4.8 hours of work, all cargo will have been moved

Answer: A. The team will have moved all the cargo in about 4.8 hours.

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students correctly find \(\mathrm{x = 4.8}\) but misinterpret what this value represents in the context. They might think the 4.8 represents the rate of work rather than the time when work is completed.

This may lead them to select Choice B (The team has been moving about 4.8 tons of cargo per hour).

Second Most Common Error:

Poor INFER skill: Students don't recognize that they need to find the x-intercept, instead focusing on other parts of the equation like the coefficient -25 or constant 120.

This may lead them to select Choice C (25 tons per hour) or Choice D (120 tons initially).

The Bottom Line:

This problem tests whether students can connect algebraic procedures (finding intercepts) with real-world interpretations. The mathematical work is straightforward, but translating the result back to context requires careful attention to what each variable represents.