Ravi obtained 70 and 75 marks in first two unit test. Find the minimum marks he should get in the third test to have an average of at least 60 marks.
Solution and Explanation
Since the student should have an average of at least 60 marks,
\(\frac{70+75+x}{3} ≥ 60\)
⇒ 145+x ≥ 180
⇒ x ≥ 180-145
⇒ x ≥ 35
Thus, the student must obtain a minimum of 35 marks to have an average of at least 6 marks.
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Concepts Used:
Inequalities
In mathematics, inequality is a relationship that compares two numbers or other mathematical expressions in a non-equal fashion. It is most commonly used to compare the size of two numbers on a number line.
Specifically, a linear inequality is a mathematical inequality that integrates a linear function. One of the symbols of inequality is observed in a linear inequality: In graph form, it represents data that is not equal.
Some of the linear inequality symbols are given below:
- < less than
- > greater than
- ≤ less than or equal to
- ≥ greater than or equal to
- ≠ not equal to
- = equal to
Inequalities can be demonstrated as questions that are solved using alike procedures to equations, or as statements of fact in the form of theorems. It is used to contrast numbers and find the range or ranges of values that pleases a variable's criteria.