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.