Proportions and Ratios: TEAS Practice Question with Answer & Explanation

Understanding Proportions in TEAS Math

This question requires you to use proportional reasoning, a frequent topic on the TEAS 7 Mathematics section. A proportion is a mathematical statement that two ratios are equal. In this scenario, the relationship between the actual building height and the model height remains constant.

The Step-by-Step Calculation

To solve for the unknown, we set up a proportion where: Actual Height ÷ Model Height = Actual Height ÷ Model Height

1. Set up the equation: Let $x$ be the height of the new model. $\frac{200 \text{ m}}{40 \text{ cm}} = \frac{625 \text{ m}}{x \text{ cm}}$

2. Cross-multiply to solve for $x$: Multiply the numerator of one side by the denominator of the other: $200 \cdot x = 40 \cdot 625$

3. Simplify the multiplication: $200x = 25,000$

4. Isolate $x$: Divide both sides by 200: $x = \frac{25,000}{200}$ $x = 125$

Therefore, the model for the 625-meter building would be 125 cm tall.

Analysis of the Options

• 125 cm (Correct): This is the result of the cross-multiplication and division process ($25,000 / 200$).
• 160 cm (Incorrect): This might result from a calculation error or misplacing numbers in the ratio (e.g., trying to find 40% of 400).
• 203.5 cm (Incorrect): This is a distractor that might occur if a student attempts to add or subtract values rather than using a ratio.
• 135 cm (Incorrect): This is a common "guess" number that doesn't follow the mathematical scale factor of 5 (200 / 40 = 5; 625 / 5 = 125).

Why Direct Proportions Matter for Nurses

In nursing school and clinical practice, you will use this exact logic for dosage calculations. For example, if a medication is supplied as 500 mg in 5 mL, and you need to administer 125 mg, you are solving a proportion: $\frac{500}{5} = \frac{125}{x}$. Mastering this now ensures safety and accuracy in your future career.

Memory Tip

When setting up a proportion, always "Keep your units in the same neighborhood." If you put Actual Height on top on the left side, you must put Actual Height on top on the right side.

• $\frac{\text{Actual}}{\text{Model}} = \frac{\text{Actual}}{\text{Model}}$ is correct.
• $\frac{\text{Actual}}{\text{Model}} = \frac{\text{Model}}{\text{Actual}}$ will lead to a wrong answer!