Frame the question in linear equation from the line
Answers
Step-by-step explanation:
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
Step-by-step explanation:
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