Question

Identify the unknown amount as the percent, part, or whole. What percent of 60 is \(24 ?\)

Short answer

Answer: 40%

Step-by-step solution

Understand the problem

We want to find the percent such that the given percent of 60 equals 24. We can represent the percent as a decimal, so let's call it x.

Set up the proportion

To set up the proportion, we will use the relationship: part = percent × whole. In this case, the part is 24, the whole is 60, and the percent is x. So, we have: \[24 = x \times 60\]

Solve for x

To find x, we will divide both sides of the equation by 60: \[x = \frac{24}{60}\] Now, simplify the fraction: \[x = \frac{2}{5}\]

Convert the decimal to a percent

To convert the fraction to a percent, we multiply it by 100: \[x = \frac{2}{5} \times 100\% = 40\%\] So, 40% of 60 is 24. In this problem, the unknown amount (40%) is the percent.

Key concepts

Part-Whole Relationship

Understanding the part-whole relationship is crucial when dealing with percent problems. In these scenarios, you're often given two quantities: a part and a whole, or a percentage and a part, and asked to find the missing piece. For instance, when asked, "What percent of 60 is 24?", you need to identify what part (24) represents in relation to the whole (60).

Think of this relationship as a pie. If the whole is the pie, the part is simply one part or slice of that pie. If 60 represents the full pie, 24 is a portion of it.

In simpler terms, you're trying to determine how big of a slice (as a percentage) 24 is from the whole pie of 60.

Proportion

Proportions are a powerful tool for solving percent problems. A proportion is an equation that states two ratios are equivalent, often used to compare parts to wholes. In our problem, you create a proportion based on the fundamental relationship:

• part = percent × whole.

For our exercise, the part is 24, the whole is 60, and the percent, which we are solving for, is represented by the variable \(x\).

Setting up the proportion helps you visualize the relationships:

• 24 (part) = \(x\) (percent as a decimal) × 60 (whole).

Using this setup allows you to solve for one unknown value when the other values are known. Think of it as a way to set one side of the equation equal to another, simplifying the path to finding the unknown percentage.

Solving Equations

Solving equations is the mathematical process used to determine an unknown value. In percent problems like this, it's about isolating the variable—commonly the unknown percentage—and finding its value. Let's look at how this is achieved step by step.

After setting up your equation based on the part-whole relationship, you have:

• \(24 = x \times 60\).

To solve for \(x\), rearrange the equation by dividing both sides by 60, allowing you to isolate \(x\):

• \(x = \frac{24}{60}\).

Next, simplify the fraction to \(\frac{2}{5}\). This gives you the percentage in decimal form. Converting this to a percentage involves multiplying by 100, so \(x = \frac{2}{5} \times 100\% = 40\%\).

This process shows how solving equations can provide a clear pathway to answers, breaking down the problem into manageable steps that reveal the missing percent value.