Ratios and Proportions: TEAS Practice Question with Answer & Explanation

Understanding Ratios in Healthcare

In nursing and healthcare, ratios are frequently used to determine staffing needs, medication dosages, and patient demographics. A ratio compares two quantities, showing how many times one value contains or is contained within the other.

Step-by-Step Calculation

To solve for the missing number in a ratio, we set up a proportion where two ratios are equal to each other.

1. Identify the Given Ratio: The problem states the ratio of Pediatric (P) to Adult (A) is 5:2. This can be written as a fraction: $\frac{5}{2}$.
2. Set Up the Proportion: We know there are 50 adults, and we need to find the number of pediatric patients ($x$). We align the units in our proportion: $$\frac{\text{Pediatric}}{\text{Adult}} = \frac{5}{2} = \frac{x}{50}$$
3. Solve for x (Cross-Multiplication): Multiply the numbers diagonally across the equals sign: $$2 \times x = 5 \times 50$$ $$2x = 250$$
4. Isolate x: Divide both sides by 2: $$x = \frac{250}{2}$$ $x = 125$

Why the Other Answers Are Incorrect

• A) 115 patients: This may result from a simple subtraction error or miscalculation during multiplication ($23 \times 5$ instead of $25 \times 5$).
• B) 120 patients: This might occur if a student tries to estimate the ratio rather than calculating the precise multiplier.
• D) 130 patients: This is a common "distractor" for students who may have misread the initial ratio or added extra units to the final total.

TEAS Math Concept: Proportions

On the TEAS 7 Math section, you are expected to solve real-world problems involving ratios and proportions. The key is ensuring that your units match across both sides of the equals sign. If "Pediatric" is on top on the left side, it must be on top on the right side.

Memory Tip

Think of a ratio like a recipe. If a recipe calls for 5 cups of flour for every 2 cups of sugar, and you decide to use 50 cups of sugar (which is 25 times the original amount), you must also multiply the flour by 25 ($5 \times 25 = 125$) to keep the "taste" the same!