There are several examples of linear equations in real life. Real-Life Problems are turned into mathematical statements to form linear equations and solve them using different methods. In this article, we have mentioned various models of Problems on Application of Linear Equations for your reference. Practice them and learn how to solve the Applications of Linear Equations Questions with the examples listed.
How to Convert a Real-Life Problem into Linear Equations?
Follow the steps mentioned below to change a real-life problem into a linear equation and solve it easily. They are as under
- Read the given statement carefully and write it in the form of an algebraic expression.
- Determine the unknown quantity to be found.
- Use the conditions and frame an equation to find the unknown variable.
- Solve the equation.
- Verify if the value obtained meets the given conditions or not.
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Applications of Linear Equations Problems with Solutions
Example 1.
The Sum of Two Numbers is 60. One Number is Thrice another Number. Find the Numbers?
Solution:
Let the numbers be x
One Number is thrice the other number 3x
Sum of two numbers = 60
x+3x=60
4x=60
x=15
Other Number = 4x
=4*15
=60
Example 2.
If a car travels from city A to city B in 6 hours and covers a distance of 900 kms, find the speed of the car?
Solution:
Let us consider the speed of car be ‘s’
Given time t = 6 hrs
We know s = d/t
s=900/6
=150 km/hr
therefore, Speed of the Car = 150km/hr
Example 3.
A daughter is one-sixth of her mother’s age at present. If after 4 years, the daughter becomes one-half of her mother’s age. Then, calculate their present ages?
Solution:
Let us take x and y as the present ages of the mother and daughter.
Now, at present daughter is one-third of her mother’s age
So, y = x/6 or x= 6y ————————-(1)
After 4years, so we add 5 to the present ages.
(y + 4) = 1/2 (x + 4)
Or, 2y + 8 = x + 4 ————————-(2)
Substituting x = 3y from equation (1) to equation (2) we get,
2y + 8 = 3y +4
3y – 2y = 8 – 4
Hence, y = 4
Now, x = 6y
So, x = 6 x 4 = 24
Hence, x = 24.
Hence the present age of the mother is 24, and that of the daughter is 4.
Example 4.
Find the number whose one-third is less than the one-seventh by 4?
Solution:
Let the unknown number be x
According to the problem, one-third of x is less than the one-seventh of x by 4
Therefore, x/3 – x/7 = 4
Multiplying both sides by 20 (LCM of denominators 4 and 5 is 20)
7x – 3x = 4*21
4x = 84
x=21
Therefore, the unknown number is 21.