Lesson 77: Percent of a Number, Part 2

New Concept

We find an unknown percent, part, or whole by translating word problems directly into equations. This turns complex questions into simple algebra.

What’s next

Next, you'll work through examples showing how to set up and solve these equations, including cases where the percent is greater than $100\%$.

Property

To find a missing percent, translate the problem into an equation:

Examples

• What percent of 80 is 20?
  $$W_p \times 80 = 20 \rightarrow W_p = \frac{20}{80} = \frac{1}{4} = 25\%$$
• What percent of 5.00 dollars is 0.40 dollars?
  $$W_p \times 5 = 0.40 \rightarrow W_p = \frac{0.40}{5} = 0.08 = 8\%$$
• Seventy is what percent of 50?
  $$70 = W_p \times 50 \rightarrow W_p = \frac{70}{50} = 1.4 = 140\%$$

Explanation

Think of yourself as a math detective cracking a code! Convert the word problem directly into a math equation. The number after 'of' is what you multiply by, and the number after 'is' is the result. Solve for the missing variable (

Property

To find the original number when you know the percent and the part, use the equation:

Examples

• Twenty percent of what number is 50?
  $$0.20 \times W_N = 50 \rightarrow W_N = \frac{50}{0.20} = 250$$
• Seventy-five percent of what number is 300?
  $$\frac{3}{4} \times W_N = 300 \rightarrow W_N = 300 \times \frac{4}{3} = 400$$
• Ninety is 150 percent of what number?
  $$1.5 \times W_N = 90 \rightarrow W_N = \frac{90}{1.5} = 60$$

Explanation

Here, the total amount is the mystery you need to solve. Start by converting the given percentage into a decimal or a fraction. Set up your equation, then use inverse operations to isolate the unknown number (

Property

Use this key to translate percent problems:

• 'What percent/number' becomes the variable ($W_p$ or $W_N$),
• 'of' becomes multiplication ($\times$),
• 'is' becomes equals ($=$).

Examples

• "What percent of 50 is 10?" translates to $W_p \times 50 = 10$.
• "Fifty is what percent of 200?" translates to $50 = W_p \times 200$.
• "Twenty percent of what number is 40?" translates to $0.20 \times W_N = 40$.

Explanation

Every percent problem is a sentence waiting to be translated into the language of math. The key is to swap specific words for math symbols. 'Of' is your cue to multiply, 'is' signals the equals sign, and 'what number' or 'what percent' is your unknown variable. Once translated, you just have a simple equation to solve for your answer.