Related Articles

# Sum of two numbers is 17 and their difference is 5. What are the numbers?

• Last Updated : 05 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 5x+3 = 7, 5x+ 3 is the left-hand side expression and 7 is the right-hand side expression connected with the ‘=’ sign.

There are mainly 3 types of equations:

• Linear 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. 5x+3=7, for example, is a linear equation with only one variable. As a result, there is only one solution to this equation, which is x = 4/5. 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.

### Sum of two numbers is 17 and their difference is 5. What are the numbers?

Solution:

Let both numbers be first and second.

According to the problem statement:

first + second = 17 (Consider this as 1st equation)
first – second = 5  (Consider this as 2nd equation)

first + second + first – second = 17 + 5
2 * first = 22
first = 22 / 2
first = 11

So from this we get first = 11, put this value in any equation i.e.

first + second = 17 (Put the value of first in this equation)
11 + second = 17
second = 17 – 11
second = 6

So, the numbers are 11 and 6.

If we consider the case i.e. second – first = 5, then the solution will be same and the first number will become 6 and second number will become 11.

### Sample Questions

Question 1: What two numbers have a sum of 19 and a difference of 15?

Solution:

Let both numbers be first and second. According to the problem statement:

first + second = 19 (Consider this as 1st equation)
first – second = 15  (Consider this as 2nd equation)

first + second + first – second = 19 + 15
2 * first = 34
first = 34 / 2
first = 17

So from this we get first = 17, put this value in any equation i.e.

first + second = 19 (Put the value of first in this equation)
17 + second = 19
second = 19 – 17
second = 2

So, the numbers are 17 and 2.

If we consider the case i.e. second – first = 15, then the solution will be same and the first number will become 2 and second number will become 17.

Question 2: What two numbers have a sum of 23 and a difference of 13?

Solution:

Let both numbers be first and second.

According to the problem statement:

first + second = 23 (Consider this as 1st equation)
first – second = 13  (Consider this as 2nd equation)

first + second + first – second = 23 + 13
2 * first = 26
first = 36 / 2
first = 18

So from this we get first = 18, put this value in any equation i.e.

first + second = 23 (Put the value of first in this equation)
18 + second = 23
second = 23 – 18
second = 5

So, the numbers are 18 and 5.

If we consider the case i.e. second – first = 13, then the solution will be same and the first number will become 5 and second number will become 18.

Attention reader! All those who say programming isn’t for kids, just haven’t met the right mentors yet. Join the  Demo Class for First Step to Coding Coursespecifically designed for students of class 8 to 12.

The students will get to learn more about the world of programming in these free classes which will definitely help them in making a wise career choice in the future.

My Personal Notes arrow_drop_up