Linear Equation Word Problem: Check Important Questions

Linear equations in one variable in Class 8 Math teach us that a mathematical equation can take many distinct forms with various variables, degrees, coefficients, and other factors. However, a mathematical expression with a polynomial whose highest power is 1 and which only has one variable is known as a linear equation in one variable.

The topics explained in this chapter strongly emphasise what a linear equation in one variable means and how to use it to solve certain problems. There are many different kinds of linear equations, as previously discussed, and each one can be solved differently. This chapter details how to convert a word problem into a linear mathematical equation and what methods to use to solve it. Continue reading this article to learn more about the linear equation word problem.

Introduction to Linear Equations

A linear equation has terms that are either constants or the result of a constant and a variable. This variable only takes the form of a single power, ax + b = 0, where a and b are constants and a ≠ 0. It is a simple example of a linear equation with only one variable, x. An equivalence containing variables is referred to as an algebraic equation. The expression is referred to as LHS (Left Hand Side) on the left and RHS (Right Hand Side) on the right.

To find a linear equation’s solution is to solve a linear equation. The three basic forms of linear equations—those with one variable, those with two variables, and those with three variables—and their respective methods to find a solution are mentioned below:

• Graphical Method
• Elimination Method
• Substitution Method
• Cross Multiplication Method
• Matrix Method
• Determinants Method

Word Problems on Linear Equation

Some of the important word problems in Linear Equation Class 8 are mentioned below to help students with their exam preparation. Students must go through these questions and try to solve them using their problem-solving skills:

Q.1. The breadth of a rectangular garden is 2/3 of its length. If its perimeter is 40 m, find its dimensions.

Q.2. The difference between two positive numbers is 40, and the ratio of these integers is 1 : 3. Find the integers.

Q.3. The sum of a two-digit number and the number obtained by reversing its digits is 121. Find the number if its unit place digit is 5.

Q.4. If the length of the rectangle is increased by 40% and its breadth is decreased by 40%, what will be the percentage change in its perimeter?

Q.5. A fruit seller buys some oranges at the rate of ₹ 5 per orange. He also buys an equal number of bananas at the rate of ₹ 2 per banana. He makes a profit of 20% on oranges and a profit of 15% on bananas. In the end, he sold all the fruits. If he earned a profit of ₹ 390, find the number of oranges.

Q.6. A steamer goes downstream from one point to another in 7 hours. It covers the same distance upstream in 8 hours. If the speed of the stream is 2 km/h, find the speed of the steamer in still water and the distance between the ports.

Q.7. There is a narrow rectangular plot. The length and breadth of the plot are in the ratio of 11:4. At the rate of Rs. 100 per meter will cost the village panchayat Rs.75000 to fence the plot. What are the dimensions of the plot?

Q.8. Jane is 6 years older than her younger sister. After 10 years, the sum of their ages will be 50 years. Find their present ages.

Q.9. Ramesh is a cashier in a Canara bank. he has notes of denominations of Rs. 100, 50 and 10 respectively. The ratio of the number of these notes is 2:3:5, respectively. The total cash with Ramesh is 4,00,000. How many notes of each denomination does he have?

Q.10. Amina thinks of a number and subtracts 5/2 from it. She multiplies the result by 8. The final result is 3 times her original number. Find the number.

Q.11. A 300 m long wire is used for fencing a rectangular plot whose length is twice its width. Find the length and breadth of the plot.

Q.12. In a class of 42 students, the number of boys is 2/5 of the number of girls. Find the number of boys and girls in the class.

Q.13. My mother is 12 years more than twice my age. After 8 years, my mother’s age will be 20 years, less than three times my age. Find my age and my mother’s age.

Q.14. Adman’s father is 49 years old. He is 5 years older than four times Adman’s age. What is Adman’s age?

Q.15. The denominator of a fraction is greater than the numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the fraction.

About Linear Equations in Class 8

When there are two or more numbers and one of them is unknown, the value of this integer can be determined using linear equations in one variable. Using the expression in equation form, it is simple to determine the value of an unknown integer. We advise students to get the most out of this chapter so they can easily solve linear equation problems in exams.

Linear equations in one variable is a critical topic in Mathematics studied in Class 8. There are five main topics in the chapter on linear equations in one variable. To ensure that you fully understand the concepts of linear equations in one variable, we advise you to go over each topic mentioned below carefully:

• Introduction
• Solving Equations Where Linear Expressions are On One Side and Numbers are On Other Side of Equation
• Applications of Linear Equations in One Variable
• Solving Equations with Variables on Both the Sides
• Reducing the Given Equations to Simpler Form

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