Question

Give some examples for word problems in linear equation in two variables...No Spam....

Answer 1

Answer:

Step-by-step explanation:

1. The sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the numbers.

Sol : 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

2.The difference between the two numbers is 48. The ratio of the two numbers is 7:3. What are the two numbers?

sol:  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

3. The length of a rectangle is twice its breadth. If the perimeter is 72 metre, find the length and breadth of the rectangle.  

Sol :  Let the breadth of the rectangle be x,  

Then the length of the rectangle = 2x

Perimeter of the rectangle = 72

2(x + 2x) = 72 ⇒ 2 × 3x = 72

⇒ 6x = 72  

⇒ x = 72/6

⇒ x = 12

We know, length of the rectangle = 2x  = 2 × 12 = 24

4. Aaron is 5 years younger than Ron. Four years later, Ron will be twice as old as Aaron. Find their present ages.  

Sol :  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.  

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

Therefore, Aaron’s present age = x - 5 = 6 - 5 = 1⇒ x = 6