what percent of 50 is 120

Guri Bee

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21-10-2024

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What Percent of 50 is 120? A Detailed Explanation

This question might seem strange at first. After all, 120 is bigger than 50! But in math, percentages are all about relative comparisons, not just absolute size. Let's break down how to find the answer.

Understanding the Basics

• Percentage: A percentage represents a fraction out of 100. So, 50% is the same as 50/100, or half of something.
• The Question: We want to know what fraction of 50 is equal to 120. This is essentially asking, "What percentage of 50 do we need to add up to get 120?"

The Calculation

1. Set up a proportion: A proportion is an equation that shows two ratios are equal. We can set up the following proportion:

   x/100 = 120/50 
   

   • x represents the unknown percentage we're looking for.
   • 120 is the larger number we're comparing to 50.
   • 100 represents the whole, as percentages are out of 100.

2. Solve for x: We can solve for x using cross-multiplication:

   x * 50 = 120 * 100
   

   • Simplifying: 50x = 12000

   • Dividing both sides by 50: x = 240

The Answer

Therefore, 120 is 240% of 50.

Why It Makes Sense

• If 50 is our baseline (100%), then 120 is twice the size of 50.
• Doubling something means increasing it by 100%, so 50 + 100% = 100.
• We then need to add another 140% (of 50) to get to 120, making the total percentage 240%.

Practical Examples

• Sales: Imagine a store is offering a 120% markup on a $50 item. The final price will be $120, which is 240% of the original price.
• Growth: A company's sales grew from $50 million to $120 million. This represents a 240% growth in sales.

Let's Summarize

Finding out what percentage of 50 is 120 is a simple calculation using proportions. Understanding the relationship between percentages and fractions is key to solving these types of problems. The result, 240%, highlights that the larger number is more than double the smaller number.