# Sum of two numbers is 20 and their difference is 4. Find the numbers

• Last Updated : 17 Aug, 2021

Arithmetic is the branch of mathematics that deals with the properties and manipulation of numbers including basic operations of maths like addition, subtraction, etc. These kinds of problems basically give a few conditions and equations are required to obtain from them such that the number of unknown variables is equal to the number of equations which will make sure that the values can be found of the variables by using some basic arithmetic operations on those equations.

Look at the problem statement below for a better understanding

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### What 2 numbers have a sum of 20 and a difference of 4?

The problem given says that 2 unknown numbers are given, whose sum is equal to 20 and the difference is 4. The first requirement is to create two equations based on the information provided, two equations will contain two unknowns and they can be easily solved either by substitution method or by elimination method, lets do a step by step solution of the problem statement,

Step-by-step explanation

Since the 2 numbers are unknown, assume them to be two natural numbers  x and y

Given: Sum of x and y=20

Therefore, it can be written as,

x+y = 20  ⇢  (1)

Given, Difference of x and y = 4

which can be written as

x−y = 4  ⇢  (2)

Now it can be observed that 2 equations are formed and there are 2 unknown variables, which implies that on performing arithmetic operations on these 2 equations, the value of the unknown variables can be easily found.

Hence, on Adding equation (1) & equation (2) we get,

2x = 24

which implies x = 12

Since, the value of x is there, put x =12 in equation (1) and get y = 8

Therefore, we have obtained the 2 numbers ⇢  The first number is 12 and the second number is 8.

### Similar Problems

Question 1: Given two numbers whose difference is 6 and the sum is 10. Find the 2 numbers.

Solution:

Step-by-step explanation:

Since the 2 numbers are unknown, assume them to be two natural numbers  x and y

Given: Difference of x and y = 6

Therefore,

x-y = 6  ⇢  (1)

Given: Sum of x and y = 10

which can be written as

x+y = 10  ⇢  (2)

Now it can be observed that 2 equations are formed and 2 unknown variables are obtained, which implies that on performing arithmetic operations on these 2 equations the value of the unknown variables can be obtained.

Hence, on Adding equation (1) & equation (2),

2x = 16

which implies x = 8

Since value of x is known, put x = 8 in equation (1) and get y = 2

Therefore, the 2 numbers ⇢  The first number is 8 and the second number is 2.

Question 2: Given two numbers whose difference is 50 and the sum is 100. Find the 2 numbers.

Solution:

Step-by-step explanation:

Since the 2 numbers are unknown, assume them to be two natural numbers  x and y

Given: Difference of x and y=50

Therefore,

x-y = 50  ⇢  (1)

Given: Sum of x and y=100

which can be written as

x+y = 100  ⇢  (2)

Now it can be observed that 2 equations are formed and 2 unknown variables are obtained, which implies that on performing arithmetic operations on these 2 equations the value of the unknown variables can be obtained.

Hence, on Adding equation (1) & equation (2),

2x = 150

which implies x = 75

Since value of x is known put x=75 in equation (1) and get y=25

Therefore, the 2 numbers ⇢ The first number is 75 and the second number is 25.

Question 3: Given two integer numbers whose difference is 100 and the sum is 30. Find the 2 numbers.

Solution:

Step-by-step explanation:

Since the 2 numbers are unknown, assume them to be two natural numbers  x and y

Given: Difference of x and y=100

Therefore,

x-y = 100  ⇢  (1)

Given: Sum of x and y = 30

which can be written as

x+y = 30  ⇢  (2)

Now it can be observed that 2 equations are formed and 2 unknown variables are obtained, which implies that on performing arithmetic operations on these 2 equations the value of the unknown variables can be obtained.

Hence, on Adding equation (1) & equation (2),

2x = 130

which implies x = 65

Since value of x is known put x = 65 in equation (1) and get y = -35

Therefore, the 2 numbers ⇢ The first number is 65 and the second number is -35.

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