How to Solve Word Problems Involving the Percentage of a Number?

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:

1. 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.
2. 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.
3. Write an equation to represent the information given in the problem.
4. Use math operations to solve for the unknown value.
5. 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.
\(\frac{6}{30}=\frac{x}{100}→6×100=30x→600=30x→600÷30=x→20=x\)