How to Solve Word Problems Involving the Percentage of a Number?
In this complete step-by-step guide, you will learn how to solve different types of word problems involving the Percentage of a Number.
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Percentages are a common concept in mathematics, and they often appear in word problems. Solving word problems involving percentages can be challenging, but it’s a valuable skill to have.
A step-by-step guide to word problems involving the percentage of a number
Since percentages have no dimensions, it is known as dimensionless numbers.
The percentage problems may have \(3\) quantities: the percent, the base, and the amount.
The percent comes with the percent symbol \((\%)\) or the word “percent.”
The base is the total amount.
The amount is part of the whole.
Here is a step-by-step guide on how to solve word problems involving percentages:
- Read the problem carefully and identify the information given. This may include the percentage, the whole, and the part. Make sure you understand what is being asked in the problem.
- Identify the keywords or phrases that indicate a percentage is involved. Words such as “percent,” “percentage,” “out of \(100\),” or “per \(100\)” are clues that a percentage is involved.
- Write an equation to represent the information given in the problem.
- Use math operations to solve for the unknown value.
- Check your answer by plugging it back into the original equation and seeing if it is true.
Word Problems Involving the Percentage of a Number – Example 1
The cinema has \(230\) seats. \(161\) seats were sold for the animated movie. What percent of seats are sold?
Solution:
161 is a part of the number \(230\).
Let \(x\) represent the percent to find a percent of \(161\) out of \(230\).
Write a proportion for \(x\) and solve.
\(\frac{161}{230}=\frac{x}{100}→161×100=230x→16100=230x→16100÷230=x→70=x\)
Word Problems Involving the Percentage of a Number– Example 2
There are \(30\) students in a class and 6 of them are girls. What percent are girls?
Solution:
\(6\) is a part of the number \(30\).
Let \(x\) represent the percent to find a percent of \(6\) out of \(30\).
Write a proportion for \(x\) and solve.
\(\frac{6}{30}=\frac{x}{100}→6×100=30x→600=30x→600÷30=x→20=x\)
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