49 Is 70 Of What Number

49 is 70% of What Number? Solving Percentage Problems

This article will guide you through solving the percentage problem: "49 is 70% of what number?" We'll break down the problem step-by-step, explaining the underlying principles and offering different methods to arrive at the solution. Understanding percentage calculations is crucial in various fields, from everyday finances to advanced mathematics. This guide will help you grasp the concept and apply it effectively.

Understanding the Problem:

The core of the problem is to find the original number (let's call it "x") from which 70% equals 49. We can represent this mathematically as an equation:

0.70x = 49

This equation states that 70% (or 0.70 as a decimal) of an unknown number (x) is equal to 49. Our goal is to solve for x.

Method 1: Algebraic Solution

This is the most straightforward method. We'll manipulate the equation to isolate x:

1. Divide both sides by 0.70: This will isolate 'x' on one side of the equation.

   x = 49 / 0.70

2. Perform the division:

   x = 70

Therefore, 49 is 70% of 70.

Method 2: Using Proportions

Proportions offer another way to solve percentage problems. We can set up a proportion:

49/x = 70/100

This proportion states that the ratio of 49 (the part) to the unknown number (the whole) is equal to the ratio of 70 (the percentage) to 100 (the whole percentage).

To solve:

1. Cross-multiply: Multiply 49 by 100 and x by 70.

   4900 = 70x

2. Divide both sides by 70:

   x = 4900 / 70

3. Perform the division:

   x = 70

Again, we find that 49 is 70% of 70.

Method 3: Using the Percentage Formula

The basic percentage formula is:

(Part / Whole) * 100 = Percentage

We know the part (49) and the percentage (70). We need to find the whole (x). Let's rearrange the formula:

Whole = (Part / Percentage) * 100

Substituting our values:

Whole = (49 / 70) * 100

Whole = 0.7 * 100

Whole = 70

This confirms our previous results: 49 is 70% of 70.

Conclusion:

We've explored three different methods to solve the problem "49 is 70% of what number?". Regardless of the method used, the answer remains the same: 70. Understanding these different approaches will equip you to tackle a wide range of percentage problems with confidence. Remember to practice regularly to solidify your understanding of percentage calculations. This skill is invaluable in various aspects of life, both personal and professional.