Write and solve a proportion to determine what percent of 120 is 54?.
The Correct Answer and Explanation is :
To determine what percent of 120 is 54, we can set up a proportion where we let ( x ) represent the unknown percentage.
The proportion will be:
[
\frac{54}{120} = \frac{x}{100}
]
Step-by-Step Solution
- Set up the proportion: The proportion represents the relationship between 54 out of 120 and the unknown percentage out of 100.
- Cross-multiply to solve for ( x ):
[
54 \cdot 100 = 120 \cdot x
]
Simplifying:
[
5400 = 120x
] - Divide both sides by 120 to isolate ( x ):
[
x = \frac{5400}{120}
]
Simplifying further:
[
x = 45
]
Therefore, 54 is 45% of 120.
Explanation
A proportion is a way to represent two ratios as being equal. In this case, we are comparing 54 out of 120 to some unknown percent (x out of 100). By cross-multiplying, we solve for the percentage in question. Cross-multiplying involves multiplying across the equal sign diagonally, setting the two products equal to each other.
To isolate the variable ( x ), we divide by 120, the remaining coefficient, resulting in ( x = 45 ). This tells us that 54 represents 45% of 120. This proportion method is a fundamental skill in percentage calculation because it allows us to see the relationship between part, whole, and percentage systematically.
Understanding proportions helps simplify real-life scenarios where you need to know how much a number represents as a part of another, like discounts, test scores, or data in reports.