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What two numbers have a sum of 19 and a difference of 5?

  • Last Updated : 17 Aug, 2021

A system was introduced to define the numbers present from negative infinity to positive infinity. The system is known as the Number system. Number system is easily represented on a number line and Integers, whole numbers, natural numbers can be all defined on a number line. The number line contains positive numbers, negative numbers, and zero.

An equation is a mathematical statement that connects two algebraic expressions of equal values with ‘=’ sign. For example: In equation 3x+2 = 5, 3x+ 2 is the left-hand side expression and 5 is the right-hand side expression connected with the ‘=’ sign.

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There are mainly 3 types of equations:

  • Linear Equation
  • Quadratic Equation
  • Polynomial Equation

Here are given two equations consisting of two variables, and to find the numbers, we have to add these two equations.
As, one equation contains both positive values and the second equation contain a positive and a negative value, and by adding both equations one variable gets canceled and we get the value of another variable.
And then using the value of the second variable we can the get value of the first variable by using any of the given equations.

So, a single equation consisting of two variables can’t be solved. 

Just adding few points related to numbers:

  • Sum of two odd numbers will always be even.
  • Sum of two even numbers will always be even.
  • Sum of one odd and one even number will always be odd.

Sum of two numbers is 19 and their difference is 5. Find the Numbers.

Solution:

Let the both numbers be first and second.

According to the problem statement:
first + second = 19 (Consider this as 1st equation)
first – second = 5  (Consider this as 2nd equation)

Add both equations:



first + second + first – second = 19 + 5
2 * first = 24
first = 24 / 2
first = 12

So from this we get first = 12, put this value in any equation i.e.

first + second = 19 (Put the value of first in this equation)
12+ second = 19
second = 19 – 12
second = 7

So, the numbers are 12 and 7.

If we consider the case i.e. second – first = 5, then the solution will be same and the first number will become 7 and second number will become 12.

Similar questions

Question 1: The sum of two numbers is 50, and the difference between the two numbers is 30. The task is to find the numbers.

Solution:

Let the both numbers be first and second.

According to the problem statement:
first + second = 50 (Consider this as 1st equation)
first – second = 30  (Consider this as 2nd equation)

Add both equations:



first + second + first – second = 50 + 30
2 * first = 80
first = 80 / 2
first = 40

So from this we get first = 40, put this value in any equation i.e.

first + second = 50 (Put the value of first in this equation)
40+ second = 50
second = 50 – 40
second = 10

So, the numbers are 40 and 10.

If we consider the case i.e. second – first = 30, then the solution will be same and the first number will become 10 and second number will become 40.

Question 2: The sum of two numbers is 33, and the difference between the two numbers is 25. The task is to find both numbers.

Solution:

Let both numbers be first and second.

According to the problem statement:
first + second = 33 (Consider this as 1st equation)
first – second = 25  (Consider this as 2nd equation)

Add both equations:

first + second + first – second = 33 + 25
2 * first = 58
first = 58 / 2
first = 29

So from this we get first = 29, put this value in any equation i.e.

first + second = 33 (Put the value of first in this equation)
29+ second = 33
second = 33 – 29
second = 4

So, the numbers are 29 and 4.

If we consider the case i.e. second – first = 25, then the solution will be same and the first number will become 4 and second number will become 29.

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