Ratios and Proportions: TEAS Practice Question with Answer & Explanation

Understanding the Constant of Proportionality

In the context of the TEAS Math section, the constant of proportionality (often represented by the variable k) describes the ratio between two quantities that are directly proportional. For this specific scenario, we are looking for the unit rate of "miles per gallon" (MPG).

The Formula

To find the constant of proportionality when given a total amount and a number of units, you use the formula: k = y / x

In this problem:

• y (the dependent variable) = 376 miles
• x (the independent variable) = 16 gallons

Step-by-Step Calculation

1. Set up the division: To find the miles per single gallon, divide the total miles by the total gallons.
   • 376 ÷ 16
2. Perform the division:
   • 16 goes into 37 twice (16 × 2 = 32).
   • Subtract 32 from 37 to get 5.
   • Bring down the 6 to make 56.
   • 16 goes into 56 exactly 3.5 times (16 × 3 = 48; 56 - 48 = 8. Add a decimal and a zero; 16 goes into 80 five times).
3. Final Result: 23.5.

Why the Other Choices Are Incorrect

• Choice A (13.5): This is likely a result of a minor calculation error during long division or incorrectly estimating the divisor.
• Choice B (24.5): This is a common "distractor" result for students who might make a subtraction error in the second step of the division process.
• Choice C (3,920.0): This result comes from multiplying 376 by 16 rather than dividing. This represents total possible miles if the van got 376 MPG (impossible for a van!), not the unit rate.
• Choice D (23.5): This is the correct quotient of 376 divided by 16.

Nursing Connection

Calculating ratios and constants is a foundational skill for nursing. You will use this exact logic when calculating IV drip rates (milliliters per hour) or dosage concentrations (milligrams per milliliter). Mastery of "unit rates" ensures patient safety!