Question

At Central Park Zoo, the ratio of sea lions to penguins is 4: 11 If there are 84 more penguins than sea lions, how many sea lions are there? a. 24 b. 36 c. 48 d. 72 e. 121

Short answer

There are 48 sea lions.

Step-by-step solution

Understanding the Ratio

The problem states that the ratio of sea lions to penguins is 4:11. This means for every 4 sea lions, there are 11 penguins.

Setting Up the Equation

Let the number of sea lions be denoted as 4x and the number of penguins be denoted as 11x, where x is a common multiplier.

Formulating the Difference

According to the problem, there are 84 more penguins than sea lions. So, we can write the equation: 11x - 4x = 84

Solving for x

Simplify the equation: 7x = 84 Now, solve for x: x = 84 / 7 x = 12

Finding the Number of Sea Lions

Since the number of sea lions is 4x, substitute the value of x: Number of sea lions = 4 * 12 = 48

Conclusion

Therefore, the number of sea lions is 48. The correct answer is c. 48.

Key concepts

ratios and proportions

Understanding ratios and proportions is key to solving many math problems, including the one in our exercise. A ratio shows the relative sizes of two or more values. In our case, we have the ratio of sea lions to penguins as 4:11.
This means for every 4 sea lions, there are 11 penguins.
Proportions are two ratios set equal to each other. Here, we see how ratios and a common multiplier work together to solve real-world problems.

algebraic equations

The use of algebraic equations is crucial in simplifying complex problems into manageable parts. We first set up equations based on the information provided:

• Let the number of sea lions be represented as 4x
• Let the number of penguins be represented as 11x

The problem also tells us that there are 84 more penguins than sea lions. From this, we formulate the equation:
11x - 4x = 84
This step reduces the problem to a simple algebraic equation, making it easier to solve.

GRE math problems

GRE math problems often test your ability to translate word problems into mathematical equations, just like in our exercise. Here’s a quick overview of how we tackled it:

• We identified the given ratio and understood what it represents.
• We translated the word problem into algebraic expressions using variables.
• We formulated and solved the equation step by step.
• Finally, we substituted our variable back to find the specific quantity asked in the problem.

By practicing these steps, you’ll improve your ability to solve similar problems on the GRE efficiently.