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

Solution:

Let 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 the same and the first number will become 10 and the second number will become 40.

Sample Problem: The sum of three numbers is 50, and the sum of the first two numbers from those three numbers is 30. 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 = 50 (Consider this as 1st equation)
first + second = 30  (Consider this as 2nd equation)

So, put the value of the 2nd equation in the 1st equation i.e.

first + second +third = 50 (Put the value of first+second in this equation)
30 + third = 50
third = 50-30
third = 20

So, the third number is 20.

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