Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityHard
A civil engineer is planning a road construction project. The total length of the road is 25.5 miles. If the crew completes 1/3 of the road in the first month and 2/5 of the remaining road in the second month, how many miles of road are still left to be constructed?
- A12.75 miles
- B8.5 miles
- C15.3 miles
- D10.2 miles
Show answer & explanationAnswer & explanation
Correct answer: D. 10.2 miles
First, calculate the length completed in the first month. Then, determine the remaining length. From that remaining length, calculate 2/5 completed in the second month, and finally, subtract that from the remaining length to find what is left.
Why the other options are wrong
- A. This is the remaining road after the first month, not after both months.
- B. This is the amount completed in the first month, not the amount remaining.
- C. This is the amount completed in the second month with respect to the total, not the remaining amount.
Sequential Fractional Changes
Sequential fractional changes involve calculating a fraction of a total, then calculating a fraction of the *remaining* amount. Each step alters the base for the next calculation.
- Each fraction applies to the current remaining quantity, not the original total.
- Requires careful step-by-step calculation.
- Common in resource allocation or consumption problems.
Memory trick: First fraction, then what's left, then another fraction of *that* amount, then what's truly left.