- 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

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# Applying the percent equation: Problem type 1

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

36 is what percent of 80?

### Solution

**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 80 = 36

This is reduced to percent equation *x%* × 80 = 36

or 0.0*x* × 80 = 36

**Step 3:**

Solving for *x*, *x* = (36 × 100)/80 = 45

So, **45%** of 80 is 36

65% of what is 39?

### Solution

**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 65% of *x* = 39

This reduces to percent equation 65% × *x* = 39

or 0.65 × *x* = 39

**Step 3:**

Solving for *x*, *x* = (39 ×100)/65 = 60

So, 65% of **60** is 39

42 is what percent of 140?

### Solution

**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 140 = 42

This is reduced to percent equation *x%* × 140 = 42

or 0.0*x* × 140 = 42

**Step 3:**

Solving for *x*, *x* = (42 ×100)/140 = 30

So, **30%** of 140 is 42.