- Finding Percents and Percent Equations
- Home
- Finding a percentage of a whole number
- Finding a percentage of a whole number without a calculator: Basic
- Finding a percentage of a whole number without a calculator: Advanced
- Applying the percent equation: Problem type 1
- Applying the percent equation: Problem type 2
- Finding a percentage of a total amount: Real-world situations
- Finding a percentage of a total amount without a calculator: Sales tax, commission, discount
- Estimating a tip without a calculator
- Writing a ratio as a percentage without a calculator
- Finding the rate of a tax or commission
- Finding the total amount given the percentage of a partial amount
- Finding a percentage of a total amount in a circle graph

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

In this lesson, we solve problems involving percent equations. Percent problems can be reduced to equations and the unknown quantity is found by solving that equation

Consider the following example problems

125% of 50.8 is what number?

**Step 1:**

In this problem, the words ‘of’, ‘is’, and ‘what’ translate to a multiplication sign ‘×’, an equal to sign ‘=’ and an unknown variable *‘x’*.

**Step 2:**

The problem is re-written as 125% of 50.8 = *x*

This reduces to percent equation 125% × 50.8 = *x*

or 1.25 × 50.8 = *x*

**Step 3:**

Solving for *x*, *x* = (1.25 × 50.8) = 63.5

So, 125% of 50.8 is **63.5**

10.78 is what percent of 19.6?

**Method 1**

**Step 1:**

In this problem, the words ‘of’, ‘is’, and ‘what’ translate to a multiplication sign ‘×’ and an equal to sign ‘=’ and an unknown variable *‘x’*.

**Step 2:**

The problem is re-written as *x* % of 19.6 = 10.78

This reduces to percent equation *x* % × 19.6 = 10.78

or 0.0*x* × 19.6 = 10.78

**Step 3:**

Solving for *x*, $x = \frac{(10.78 \times 100)}{19.6} = 55%$

So, 55% of 19.6 is 39

**Method 2**

10.78 = *x*% × 19.6

10.78/19.6 = $x = \frac{(x\% \times 19.6)}{19.6} = x$

*x* = 0.55; converting the decimal to percent we get

*x* = 0.55 = 55%

What is 90% of 218?

**Step 1:**

In this problem, the words ‘of’, ‘is’, and ‘what’ translate to a multiplication sign ‘×’ and an equal to sign ‘=’ and an unknown variable *‘x’*.

**Step 2:**

The problem is re-written as 90% of 218 = *x*

This is reduced to percent equation 90% × 218 = *x*

or 0.90 × 218 = *x*

**Step 3:**

Solving for *x*, *x* = (0.90 × 218) = 196.2

So, 90% of 218 is **196.2**

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