Proportions and Ratios: TEAS Practice Question with Answer & Explanation

Understanding Ratios and Proportions

This question tests your ability to solve proportional reasoning problems, a core competency in the TEAS 7 Math section. In nursing, you will frequently use this skill for dosage calculations, such as determining how many milliliters of a medication are needed based on a patient's weight or a specific concentration.

The Step-by-Step Calculation

To solve this, we set up a proportion where the ratio of peppers to servings remains constant:

1. Set up the initial ratio: $\frac{12 \text{ oz}}{10 \text{ servings}}$
2. Set up the equivalent ratio with the unknown ($x$): $\frac{100 \text{ oz}}{x \text{ servings}}$
3. Create the proportion equation: $$\frac{12}{10} = \frac{100}{x}$$
4. Cross-multiply to solve for $x$: $$12 \times x = 10 \times 100$$ $$12x = 1,000$$
5. Isolate $x$ by dividing both sides by 12: $$x = \frac{1,000}{12}$$ $$x = 83.333...$$

Rounding to the Nearest Whole Number

The question asks for the answer to the nearest whole number. Since the decimal is $.3$ (which is less than $.5$), we round down.

• Result: 83 servings.

Analysis of Incorrect Answers

• Choice A (67 servings): This result occurs if you accidentally invert the ratio ($\frac{10}{12} \times 80$) or make a calculation error during division.
• Choice C (98 servings): This is a "distractor" value that might be reached if a student tries to subtract or add differences rather than using multiplication/division ratios.
• Choice D (104 servings): This number is slightly higher than the total ounces available. If 12 oz makes 10 servings, it is impossible for 100 oz to make more than 100 servings, as the ratio is greater than 1:1.

TEAS Math Concept: Unit Rates

An alternative way to solve this is to find the unit rate.

• $12 \div 10 = 1.2$ ounces per serving.
• Then, divide the total available ounces by the unit rate: $100 \div 1.2 = 83.33$. Both methods are valid and will lead you to the same answer! Regardless of the method, always double-check if your answer "makes sense" (e.g., if you have about 10 times the peppers, you should have about 10 times the servings).