Make 10 word problems on Linear Equations in one variable based on daily life situations and solve them..
Answers
Step-by-step application of linear equations to solve practical word problems:
1. The sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the numbers.
Solution:
Then the other number = x + 9
Let the number be x.
Sum of two numbers = 25
According to question, x + x + 9 = 25
⇒ 2x + 9 = 25
⇒ 2x = 25 - 9 (transposing 9 to the R.H.S changes to -9)
⇒ 2x = 16
⇒ 2x/2 = 16/2 (divide by 2 on both the sides)
⇒ x = 8
Therefore, x + 9 = 8 + 9 = 17
Therefore, the two numbers are 8 and 17.
2.The difference between the two numbers is 48. The ratio of the two numbers is 7:3. What are the two numbers?
Solution:
Let the common ratio be x.
Let the common ratio be x.
Their difference = 48
According to the question,
7x - 3x = 48
⇒ 4x = 48
⇒ x = 48/4
⇒ x = 12
Therefore, 7x = 7 × 12 = 84
3x = 3 × 12 = 36
Therefore, the two numbers are 84 and 36.
3. The length of a rectangle is twice its breadth. If the perimeter is 72 metre, find the length and breadth of the rectangle.
Solution:
Let the breadth of the rectangle be x,
Then the length of the rectangle = 2x
Perimeter of the rectangle = 72
Therefore, according to the question
2(x + 2x) = 72
⇒ 2 × 3x = 72
⇒ 6x = 72
⇒ x = 72/6
⇒ x = 12
We know, length of the rectangle = 2x
= 2 × 12 = 24
Therefore, length of the rectangle is 24 m and breadth of the rectangle is 12 m.
4. Aaron is 5 years younger than Ron. Four years later, Ron will be twice as old as Aaron. Find their present ages.
Solution:
Let Ron’s present age be x.
Then Aaron’s present age = x - 5
After 4 years Ron’s age = x + 4, Aaron’s age x - 5 + 4.
According to the question;
Ron will be twice as old as Aaron.
Therefore, x + 4 = 2(x - 5 + 4)
⇒ x + 4 = 2(x - 1)
⇒ x + 4 = 2x - 2
⇒ x + 4 = 2x - 2
⇒ x - 2x = -2 - 4
⇒ -x = -6
⇒ x = 6
Therefore, Aaron’s present age = x - 5 = 6 - 5 = 1
Therefore, present age of Ron = 6 years and present age of Aaron = 1 year.
5. A number is divided into two parts, such that one part is 10 more than the other. If the two parts are in the ratio 5 : 3, find the number and the two parts.
Solution:
Let one part of the number be x
Then the other part of the number = x + 10
The ratio of the two numbers is 5 : 3
Therefore, (x + 10)/x = 5/3
⇒ 3(x + 10) = 5x
⇒ 3x + 30 = 5x
⇒ 30 = 5x - 3x
⇒ 30 = 2x
⇒ x = 30/2
⇒ x = 15
Therefore, x + 10 = 15 + 10 = 25
Therefore, the number = 25 + 15 = 40
The two parts are 15 and 25.
More solved examples with detailed explanation on the word problems on linear equations.
6. Robert’s father is 4 times as old as Robert. After 5 years, father will be three times as old as Robert. Find their present ages.
Solution:
Let Robert’s age be x years.
Then Robert’s father’s age = 4x
After 5 years, Robert’s age = x + 5
Father’s age = 4x + 5
According to the question,
4x + 5 = 3(x + 5)
⇒ 4x + 5 = 3x + 15
⇒ 4x - 3x = 15 - 5
⇒ x = 10
⇒ 4x = 4 × 10 = 40
Robert’s present age is 10 years and that of his father’s age = 40 years.
7. The sum of two consecutive multiples of 5 is 55. Find these multiples.
Solution:
Let the first multiple of 5 be x.
Then the other multiple of 5 will be x + 5 and their sum = 55
Therefore, x + x + 5 = 55
⇒ 2x + 5 = 55
⇒ 2x = 55 - 5
⇒ 2x = 50
⇒ x = 50/2
⇒ x = 25
Therefore, the multiples of 5, i.e., x + 5 = 25 + 5 = 30
Therefore, the two consecutive multiples of 5 whose sum is 55 are 25 and 30.
8. The difference in the measures of two complementary angles is 12°. Find the measure of the angles.
Solution:
Let the angle be x.
Complement of x = 90 - x
Given their difference = 12°
Therefore, (90 - x) - x = 12°
⇒ 90 - 2x = 12
⇒ -2x = 12 - 90
⇒ -2x = -78
⇒ 2x/2 = 78/2
⇒ x = 39
Therefore, 90 - x = 90 - 39 = 51
Therefore, the two complementary angles are 39° and 51°
9. The cost of two tables and three chairs is $705. If the table costs $40 more than the chair, find the cost of the table and the chair.
Solution:
The table cost $ 40 more than the chair.
Let us assume the cost of the chair to be x.
Then the cost of the table = $ 40 + x
The cost of 3 chairs = 3 × x = 3x and the cost of 2 tables 2(40 + x)
Total cost of 2 tables and 3 chairs = $705
Therefore, 2(40 + x) + 3x = 705
80 + 2x + 3x = 705
80 + 5x = 705
5x = 705 - 80
5x = 625/5
x = 125 and 40 + x = 40 + 125 = 165
Therefore, the cost of each chair is $125 and that of each table is $165.
10. If 3/5 ᵗʰ of a number is 4 more than 1/2 the number, then what is the number?
Solution:
Let the number be x, then 3/5 ᵗʰ of the number = 3x/5
Also, 1/2 of the number = x/2
According to the question,
3/5 ᵗʰ of the number is 4 more than 1/2 of the number.
⇒ 3x/5 - x/2 = 4
⇒ (6x - 5x)/10 = 4
⇒ x/10 = 4
⇒ x = 40
The required number is 40.
Try to follow the methods of solving word problems on linear equations and then observe the detailed instruction on the application of equations to solve the problems.
Answer:
V+गजगामिनी नमस्ते है कि वे अपने घर में पावर cut था