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.