Solution to the Problem: If 75% of a Number is 60, What is the Number?
Mathematics often involves solving for unknowns, requiring us to manipulate numbers and equations to find the solution. The problem given here is to find the number when 75% of it is 60. Let's break down the problem using various methods to arrive at the answer and explain the steps to ensure a clear understanding.
Method 1: Basic Algebra
Let the unknown number be x. We know that 75% of x equals 60. We can write this as an equation:
75% × x 60
Expressing 75% as a fraction, we get:
75/100 × x 60
Now, let's isolate x by performing the necessary algebraic operations:
x 60 × 100 ÷ 75
x 6000 ÷ 75
x 80
To verify our calculations, we can substitute 80 back into the original equation:
75% of 80 75/100 × 80 60
This confirms that our calculation is correct.
Method 2: Proportional Reasoning
Another approach involves using proportions. If 75% is equal to 60, we can set up a proportion to find the whole number. We write:
75:100 :: 60:x
Using the property of proportions, we have:
75x 100 × 60
75x 6000
Now, solve for x:
x 6000 ÷ 75
x 80
Again, we can verify our solution by substituting 80 back into the proportion:
75:100 :: 60:80
This confirms that 80 is the correct answer.
Method 3: Logical Reasoning
Sometimes, problems can be solved using logical reasoning. As a percentage represents a fraction of a whole, 75% represents three-quarters (3/4) of the total. If 75% (three-quarters) of the number is 60, we can think of it as:
1/4 of the number 20 (since 60 ÷ 3 20)
Therefore, the whole number (100%) would be:
4 × 20 80
This logical approach also concludes that the answer is 80.
Conclusion
In all methods, the solution to the problem is 80. Whether through algebraic manipulation, proportional reasoning, or logical deduction, the process of solving for the unknown number is clarified. These methods not only provide the answer but also help develop a deeper understanding of the underlying mathematical concepts.
Keywords
percentage, calculation, problem-solving