Solving for X: If 10 is 20% of X, What is the Value of X?
In this article, we will walk through the steps of solving the equation “If 10 is 20% of X, what is the value of X?” This is a common problem in mathematics that involves understanding percentages and algebraic manipulation.
Understanding the Problem
The problem states that 10 is 20% of X. In mathematical terms, we can express this as:
10=20%×X10 = 20\% \times X
This means that 10 is equal to 20% of some unknown value, which we need to solve for. To make the calculation simpler, we’ll first convert 20% into its decimal form.
Step 1: Convert Percentage to Decimal
To convert 20% into a decimal, divide 20 by 100:
20%=20100=0.2020\% = \frac{20}{100} = 0.20
So, the equation becomes:
10=0.20×X10 = 0.20 \times X
Step 2: Solve for X
Now, we need to isolate X. To do this, divide both sides of the equation by 0.20:
X=100.20X = \frac{10}{0.20}
Step 3: Perform the Division
Next, divide 10 by 0.20:
X=100.20=50X = \frac{10}{0.20} = 50
Step 4: Conclusion
Thus, the value of X is 50.
Verification
To verify, we check if 20% of 50 equals 10:
20%×50=0.20×50=1020\% \times 50 = 0.20 \times 50 = 10
Since the original statement holds true, our solution is correct.
Summary
The value of X is 50. This process demonstrates how to solve a simple percentage problem by converting the percentage into a decimal and using basic algebra to isolate the variable.