150 is 25% of what number?
The Correct Answer and Explanation is:
To find out what number 150 is 25% of, we can set up the equation using the relationship between percentages and numbers. The equation can be represented as:
[
\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100
]
In this case, we know the part (150) and the percentage (25%), but we need to find the whole (let’s denote it as ( x )):
[
25 = \frac{150}{x} \times 100
]
To solve for ( x ), we first rearrange the equation to isolate ( x ):
- Start by multiplying both sides by ( x ) to eliminate the fraction:
[
25x = 150 \times 100
]
- This simplifies to:
[
25x = 15000
]
- Next, divide both sides by 25 to solve for ( x ):
[
x = \frac{15000}{25}
]
- Performing the division:
[
x = 600
]
Thus, 150 is 25% of 600.
Explanation
This problem illustrates the relationship between a part, a whole, and a percentage. Percentages represent a fraction of 100, which allows us to compare proportions easily. In our case, we determined that the number 150 represents a quarter (25%) of another number.
To conceptualize this, if you think of 600 divided into four equal parts, each part would represent 25% of the total, and one of those parts equals 150. This relationship is foundational in understanding how percentages work in mathematics, often used in various real-life scenarios such as financial calculations, statistical analysis, and even in everyday decisions like discounts and budgeting.
The formula we used can be applied universally. Whenever you know the part and the percentage, you can find the whole by rearranging the equation accordingly. Mastery of these calculations aids in making informed decisions and understanding numerical relationships in a broad range of contexts.