Unit 4: More Working with Percent
Topic B: Finding a Number when a Percent of it is Given
In problems when a certain percentage of a number is given, the missing term is the whole. You will be told the % and the part (is), and asked to find the whole (of), which is 100%.
Example A
20% of what number is 14?
- The part = 14
- The whole (“what number”) = unknown (call it N)
- The percent = 20%
- Write the proportion:
[latex]\dfrac{14}{\textit{N}} = \dfrac{20}{100}[/latex] - Solve the proportion:
- Simplify:
[latex]\dfrac{14}{\textit{N}} = \dfrac{\cancel{20}1}{\cancel{100}5}[/latex] - [latex]\dfrac{14}{\textit{N}} = \dfrac{1}{5}[/latex]
- Cross-multiply to solve:
[latex]\begin{equation}\begin{split} 14\times5 &= \textit{N}\times1 \\ 70 &= \textit{N} \end{split}\end{equation}[/latex][latex]20\%\text{ of }70 = 14[/latex]
- Simplify:
Check by finding 20% of 70. The answer should be 14.
[latex]\begin{equation}\begin{split} \dfrac{20}{100} &= \dfrac{\textit{N}}{70} \\ 140 &= 100\textit{N} \\ 14 &= \textit{N} \end{split}\end{equation}[/latex]
Example B
33⅓% of is 60.
- Part = 60
- Whole = N
- Percent = 33⅓% = ⅓
Set up proportion:
[latex]\begin{equation}\begin{split} \dfrac{60}{\textit{N}} &= \dfrac{1}{3} \\ 3\times60 &= \textit{N}\times1 \\ 180 &= \textit{N} \end{split}\end{equation}[/latex]
33⅓% of 180 is 60.
To check the answer, find 33⅓% of 180. The answer should be 60.
Exercise 1
Set up the proportion. Do not solve the question.
- 18 is 50% of what number?
- 24 is 15% of what number?
- 200% of what number is 86?
- 66⅔% of what number= 500?
Answers to Exercise 1
- [latex]\dfrac{18}{\textit{P}}=\dfrac{50}{100}[/latex]
- [latex]\dfrac{24}{\textit{N}}=\dfrac{15}{100}[/latex]
- [latex]\dfrac{86}{\textit{P}}=\dfrac{200}{100}[/latex]
- [latex]\dfrac{500}{\textit{P}}=\dfrac{66\tfrac{2}{3}}{100}[/latex] or [latex]\dfrac{2}{3}[/latex]
Exercise 2
Solve the following. Check your answers to see if you set up the proportion correctly.
- 60 is 75% of what number?
- 950 is 95% of:
- 125 = 33⅓% of what number?
- 120% of is 6.
- 270 is 100% of what number?
Answers to Exercise 2
- [latex]\dfrac{60}{\textit{X}}=\dfrac{75}{100},\text{ } 80[/latex]
- [latex]\dfrac{950}{\textit{P}}=\dfrac{95}{100},\text{ } 1,000[/latex]
- [latex]\dfrac{125}{\textit{N}}=\dfrac{33\tfrac{1}{3}}{100},\text{ } 375[/latex]
- [latex]\dfrac{120}{100}=\dfrac{6}{\textit{J}}, \text{ }5[/latex]
- [latex]\dfrac{100}{100}=\dfrac{270}{\textit{N}}, \text{ }270[/latex]
Exercise 3
Solve the questions.
- 480 is 66⅔% of .
- 40% of is 50.
- 33⅓% of what number is 99?
- 3 is 150% of what number?
- 122 is 80% of .
Answers to Exercise 3
- [latex]720[/latex]
- [latex]125[/latex]
- [latex]297[/latex]
- [latex]2[/latex]
- [latex]152.5[/latex]
Solving Problems when the Percent of a Number is Given
Read the problems carefully. More than one step may be needed. Look at the wording so you will recognize problems missing the whole and be able to tell them from problems missing the part.
Exercise 4
Solve the problems. Round