Question

How do you solve word problems involving percent?

Answer 1

Hint: We are given a word problem. We have to solve the word problem. First, write the mathematical expression for the word problem. Then, replace the percentage symbol by 100 at the denominator of the number. Then, solve for the required variable.

Complete step-by-step solution:
Given a word problem.
The percent marks secured by Karan in examinations is $85\% $. If the marks scored by him are $425$. Then, calculate the maximum marks.
Now, we will start by forming an equivalent mathematical expression for the word problem.
Here, let the maximum marks be X.
It is given that $85\% $ of maximum marks is equal to $425$ marks.
$ \Rightarrow 85\% {\text{ of X}} = 425$
Now, we will replace percent symbol by inserting 100 at the denominator of 85, and replace it by multiplication symbol.
$ \Rightarrow \dfrac{{85}}{{100}} \times {\text{X}} = 425$
Now, we will multiply both sides of the equation by $\dfrac{{100}}{{85}}$.
$ \Rightarrow \dfrac{{100}}{{85}} \times \dfrac{{85}}{{100}} \times {\text{X}} = \dfrac{{100}}{{85}} \times 425$
Now, solve for X.
$ \Rightarrow {\text{X}} = \dfrac{{100}}{{85}} \times 425$
$ \Rightarrow {\text{X}} = 100 \times 5$
$ \Rightarrow {\text{X}} = 500$
Thus, the maximum marks is 500.
Hence the word problem on percent can be solved by first converting it into mathematical expression and then solving for the variable.

Note: The students must remember that in such types of questions it’s important to read the word problem carefully and must separate relevant and irrelevant information carefully and then convert the equation in mathematical form. The percent problems are basically classified into three types.
Consider the statement, “a percent of b is equal to c”
Then, the first type of problem where the value of a is to be determined.
The second type of problem involves the identification of the value of b
In the third type of problems, the value of c is unknown