Sum of two numbers is 18 and their difference is 8. Find the numbers

Problem Statement: What two numbers have a sum of 18 and a difference of 8?

Solution:

Given,

• Sum of the two numbers is 18.
• Difference between the two numbers is 8.

According to the given conditions let the First number be x and the second number be y.

so the equation becomes,

x + y = 18 —–> (i)

x – y = 8 —–> (ii)

adding both equations (i) and (ii) we get,

2x = 26

x = 13 —–>(iii)

putting the value of x in equation 1 we get,

x + y = 18

13 + y = 18

y = 18-13

y = 5

so, the numbers are 13 and 5

value of

• x = 13
• y = 5

Sample Questions

Question 1: The sum of three numbers is 33, and the sum of the first two numbers from those three numbers is 19. The task is to find the third number.

Solution:

Let the numbers be first, second and third.

According to the problem statement:

first + second + third = 33 (Consider this as 1st equation)

first + second = 19  (Consider this as 2nd equation)

So, put the value of 2nd equation in 1st equation i.e.

first + second +third = 33 (Put the value of first+second in this equation)

19 + third = 33

third = 33 – 19

third = 14

So, the third number is 14.

Question 2: What two numbers have a sum of 30 and a difference of 8?

Solution:

Let the both numbers be first and second.

According to the problem statement:

first + second = 30(Consider this as 1st equation)

first – second = 8  (Consider this as 2nd equation)

Add both equations:

first + second + first – second = 30 + 8

2 × first = 38

first = 38 / 2

first = 19

So from this we get first = 19, put this value in any equation i.e.

first + second = 30 (Put the value of first in this equation)

19 + second = 30

second = 30 – 19

second = 11

So, the numbers are 19 and 11.

If we consider the case i.e. second – first = 8, then the solution will be same and the first number will become 11 and second number will become 19.