Explain how to use equivalent ratios to find 125% of 200
The Correct Answer and Explanation is:
To find 125% of 200 using equivalent ratios, start by understanding that 125% means 125 out of 100. This creates the ratio: 125100=x200\frac{125}{100} = \frac{x}{200}100125=200x
The goal is to determine the value of xxx, which represents 125% of 200. To solve for xxx, use cross multiplication: 125×200=100×x125 \times 200 = 100 \times x125×200=100×x 25000=100×25000 = 100×25000=100x
Now, divide both sides by 100: x=25000100=250x = \frac{25000}{100} = 250x=10025000=250
So, 125% of 200 is 250.
This method uses the concept of equivalent ratios to express the relationship between percentages and whole numbers. A percentage represents a part per hundred. Therefore, 125% can be written as the ratio 125:100. This ratio indicates how a value compares to 100 and can be scaled up or down to find equivalent values for different wholes.
By setting up the proportion 125100=x200\frac{125}{100} = \frac{x}{200}100125=200x, the relationship remains consistent. Cross multiplying maintains equality and allows isolation of the unknown variable. This technique is especially helpful when dealing with percentages that are not easy to calculate mentally.
Equivalent ratios are powerful because they simplify complex comparisons into solvable equations. In this case, the ratio form translates a percentage problem into a linear equation. Once the equation is solved, the result shows that 125% of 200 equals 250. This method avoids the need for memorizing specific formulas and instead relies on understanding relationships between numbers.
Using ratios in percentage calculations ensures accuracy and builds a strong foundation for solving more advanced problems, including those involving proportions, scaling, and real-world applications like finance or statistics.
