Question

Mr. Burke’s class has twice as many girls as boys. If half of the boys and a quarter of the girls are in the chess club, what is the ratio of girls to boys who are in the chess club? (A) 4:1 (B) 2:1 (C) 1:1 (D) 1:2

Short answer

The ratio of girls to boys who are in the chess club is 1:1 (C).

Step-by-step solution

Determine the number of boys and girls in the chess club using given ratios

Let's assume that the number of boys in the class is \(b\), and the number of the girls is \(2b\) as the ratio is 2:1. According to the problem, half of the boys and a quarter of the girls are in the chess club. So, there are \(0.5b\) boys and \(0.25*2b = 0.5b\) girls in the chess club.

Find the ratio of girls to boys in the chess club

We know that the number of boys and girls in the chess club are both \(0.5b\). Hence, the ratio of girls to boys in the chess club is \(0.5b : 0.5b\), which simplifies to 1:1 stated in option (C). So, the correct answer is (C) 1:1. The ratio of the girls to boys who are in the chess club is equal.

Key concepts

GED Math Practice

When preparing for the GED math test, practicing ratio word problems is absolutely essential. Ratio problems often involve proportional reasoning, which is a key skill evaluated in the GED math section. Understanding ratios is fundamental in topics such as scale drawings, probability, and similarity in geometry.

It's crucial for students to become familiar with translating words into mathematical expressions and to do so, they should engage with a variety of problems. Exercises like the one involving Mr. Burke’s class require you to apply ratio understanding in a real-world context. For GED practice, go beyond the mechanics and make sure to justify each step logically to reinforce comprehension. Keeping a list of steps, like identifying what the ratio represents and applying given conditions to find the desired ratio, aids in structured learning and review.

Ratio and Proportion

Ratio and proportion are foundational concepts in mathematics used to compare quantities and maintain relationships between quantities when they scale up or down. A ratio is a comparison of two quantities that specifies how many times one value contains another, and it is often expressed in the form of 'a to b' or as a fraction \( a/b \).

Proportions, on the other hand, state that two ratios are equal, expressing a consistent relationship between four quantities. In the exercise about Mr. Burke’s class, understanding that the ratio of girls to boys is initially 2:1 allows us to determine how this ratio is affected when a quarter of the girls and half of the boys join a club. The crucial step here is to recognize that both numbers of students in the chess club are directly related to the original number of boys, and thus, both can be expressed with 'b'. This allows us to simplify the resulting ratio.

Math Word Problem Solving

Math word problems can seem daunting, but breaking them down into smaller steps makes them more approachable. Start by carefully reading the problem to understand what is being asked. Next, identify relevant information and disregard any distractors. Then, choose the proper mathematical operations needed to solve the problem, drawing on your knowledge of algebra, geometry, or arithmetic.

For instance, in the provided textbook solution, we begin by defining variables for the unknowns (number of boys and girls). We then use the information provided to establish relationships between these variables. Finally, we calculate the desired ratio by simplifying the mathematical expression we've derived. Ensuring students understand the reasoning behind each step, and not just the computation, is key to mastering math word problems.