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Sum of two numbers is 18 and their difference is 8. Find the numbers

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  • Last Updated : 05 Aug, 2021
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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.

There are mainly 3 types of equations:

  • Linear Equation
  • Quadratic Equation
  • Polynomial Equation

Here, we will study about the Linear equations.

Linear equations in one variable are equations that are written as ax + b = 0, where a and b are two integers and x is a variable, and there is only one solution. 3x+2=5, for example, is a linear equation with only one variable. As a result, there is only one solution to this equation, which is x = 3/11. A linear equation in two variables, on the other hand, has two solutions.

A one-variable linear equation is one with a maximum of one variable of order one. The formula is ax + b = 0, using x as the variable.

There is just one solution to this equation. Here are a few examples:

  • 4x = 8
  • 5x + 10 = -20
  • 1 + 6x = 11

Linear equations in one variable are written in standard form as:

ax + b = 0

Here,

  • The numbers ‘a’ and ‘b’ are real.
  • Neither ‘a’ nor ‘b’ are equal to zero.

Solving Linear Equations in One Variable

The steps for solving an equation with only one variable are as follows:

Step 1: If there are any fractions, use LCM to remove them.

Step 2: Both sides of the equation should be simplified.

Step 3: Remove the variable from the equation.

Step 4: Make sure your response is correct.

Problem Statement: What two numbers have a sum of 18 and a difference of 8?

Solution:

Let both numbers be first and second.

According to the problem statement:

first + second = 18 (Consider this as 1st equation)
first – second = 8  (Consider this as 2nd equation)

Add both equations:

first + second + first – second = 18 + 8
2 * first = 26
first = 26 / 2
first = 13

So from this we get first = 13, put this value in any equation i.e.

first + second = 18 (Put the value of first in this equation)
13 + second = 18
second = 18 – 13
second = 5

So, the numbers are 13 and 5.

If we consider the case i.e. second – first = 8, then the solution will be same and the first number will become 5 and second number will become 13.

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.

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