Sum of two numbers is 17 and their difference is 5. What are the numbers?
If sum of two numbers is 17 and their difference is 5 then the two numbers are either 6 and 11 or 11 and 6.
Let us suppose the numbers are x and y then the two equations formed by the above statement are x + y = 17 and |x – y| = 5. This is a linear equation in two variables x and y.
Problem: Sum of two numbers is 17 and their difference is 5. What are the numbers?
Solution:
Let us suppose, the two numbers are:
x and y
According to the question,
- x + y = 17…(i)
- x – y = 5…(ii)
Now, subtract the equation (i) by equation (ii), we get
(x + y) – (x – y) = 17 – 5
x + y – x + y = 12
2y = 12
y = 6
Now, putting the value of y = 6 in equation (ii), we get
x – 6 = 5
x = 11
Therefore, the required two numbers are 11 and 6.
So, the two numbers that have a sum of 17 and a difference of 5 is 11 and 6.
Another Method
Sum of two numbers is 17 and their difference is 5. What are the numbers?
Here, we use Substitution method to solve this equation.
x + y = 17…(i)
x – y = 5…(ii)
From equation (i), we get
y = 17 – x…(iii)
Now, substitute the value of y in equation (ii), we get
x – (17 – x) = 5
x – 17 + x = 5
2x = 22
x = 11
Here, substitute the value of x in equation (1), we get
x + y = 17
11 + y = 17
y = 6
Therefore, the required two numbers are 11 and 6 respectively.
Last Updated :
19 Mar, 2024
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