Question

Linear equation word problems with solution

Answer 1

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.