Problem 50 - Algebra 1

Question

Write and solve an equation to answer the question. About one eighth of the population is left-handed. In what size school would you expect to find about 50 left-handed students?

Step-by-Step Solution

Answer

So, a school of 400 students would have about 50 left-handed students.

Step 1: Equation Setup

Let \(X\) be the total school size. The question tells us that one eighth of the population is left-handed: \(\frac{1}{8} * X\), and that there are about 50 left-handed students. So, the equation becomes: \(\frac{1}{8} * X = 50\).

Step 2: Solve the equation

We need to isolate \(X\) on one side of the equation. So, we'll multiply each side by 8: \(X = 50 * 8\).

Step 3: Calculate

Now, calculate the right side of the equation: \(X = 400\).

Key Concepts

Proportion

Proportion is a mathematical concept that helps us compare parts to a whole. It's like asking, "How much is this piece of the pie relative to the entire pie?" In this problem, we're looking at left-handed students as a part of the whole school population.

Here's how it works in simple terms: imagine the entire school as one big group. Proportion tells us that one part of this group, the left-handed students, makes up one eighth of the total. This means if you divide the school into eight equal parts, one of those parts is expected to be left-handed students.

Using proportions can make it easy to estimate or predict outcomes based on known ratios, just as we did here to find out the full school size when we know about how many students are left-handed.

Left-handed Students

Left-handed students are individuals who naturally use their left hand for writing and other tasks more than their right hand. While the majority of the population is right-handed, around 10-12% are left-handed.

This proportion is important not only for curiosity but also for planning educational resources. For example, schools may need left-handed desks or supplies for these students.

In this exercise, we considered a standard approximation where one eighth of any given population could be left-handed, which helps us use simple math to plan for their needs.

School Population

School population refers to the total number of students enrolled in a school. When we analyze specific demographics, like left-handed students, we often express these groups as a part of the total population.

To find how large a school's population is, given a known number of left-handed students, we can use ratios. This helps us make predictions without needing to count each student individually.

For instance, by knowing that 50 left-handed students are about one eighth of the school's population, we can reverse-engineer to find the total population. This is essential for planning things like classroom sizes, resources, and even facilities.

Algebraic Equation

An algebraic equation is a mathematical statement that shows the equality of two expressions. In this problem, we used an equation to relate the number of left-handed students to the total school size.

We set up the equation \[ \frac{1}{8} \times X = 50 \] to represent the scenario and used algebraic methods to solve it.

Algebra helps us manipulate equations to find unknown values, like the total school population. By isolating the variable (in this case, \(X\), the total school size) on one side, we provide a solution using logical steps. This approach is versatile and can solve a broad range of mathematical problems by breaking them down into manageable parts.