65% of what number is 39?
The Correct Answer and Explanation is :
To find the number where 65% equals 39, we can set up an equation based on the concept that 65% of a number (let’s call it ( x )) is equal to 39. Here’s how you can solve it:
Step 1: Set Up the Equation
The equation for “65% of ( x ) is 39” can be written as:
[
0.65 \times x = 39
]
Step 2: Solve for ( x )
To isolate ( x ), divide both sides by 0.65:
[
x = \frac{39}{0.65}
]
Calculating this:
[
x = 60
]
So, the number is 60.
Explanation (300 words)
This question involves finding a base number when a certain percentage of it is known. In this case, 65% of some unknown number is given as 39. To solve problems like this, it’s helpful to remember the concept of percentages. “Percent” means “per hundred,” so 65% translates to 65 per 100, or 0.65 in decimal form.
By setting up the equation ( 0.65 \times x = 39 ), we model the problem mathematically. Here, ( x ) represents the unknown base number we’re trying to find. Solving for ( x ) requires us to isolate ( x ) on one side of the equation, so we divide both sides by 0.65.
This approach is generally applicable in problems involving percentages. Whenever you know a part of a whole and a percentage, you can always set up an equation to find the whole by dividing the part by the percentage (in decimal form). Similarly, if you know the whole and need to find the part represented by a percentage, you multiply instead.
Understanding the process behind these calculations is valuable for many real-world situations, such as calculating discounts, understanding statistics, or determining ratios in work or school problems. Practicing this method builds confidence with both percentages and basic algebra, making it easier to approach similar problems in the future.