The sum of two numbers is 50, and their difference is 30. Find the numbers.
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, 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
- 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.
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.
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.