 Math »
 The sum of a two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there
The sum of a two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there
Explore the mathematical enigma: a twodigit number and its reverse sum up to 66. Hunt down the number with digits differing by 2 and unveil the total count of such numbers.
by Maivizhi A
Updated Feb 24, 2024
The sum of a two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?
There are two such numbers: 24 and 42.
Let's denote the twodigit number as 10a + b, where a is the digit in the tens place and b is the digit in the ones place. The number obtained by reversing the digits is 10b + a.
According to the given conditions:

The sum of the original number and the number obtained by reversing the digits is 66, so we have the equation: (10a + b) + (10b + a) = 66

The digits of the number differ by 2, so we have the equation: a  b = 2
Now, let's solve this system of equations:
From the second equation, we have two cases:
 a  b = 2
 b  a = 2
Case 1: a  b = 2
Substitute a = b + 2 into the first equation: (10(b + 2) + b) + (10b + (b + 2)) = 66 (10b + 20 + b) + (10b + b + 2) = 66 22b + 22 = 66 22b = 44 b = 2 a = b + 2 = 4
So, one such number is 42.
Case 2: b  a = 2
Substitute b = a + 2 into the first equation: (10a + (a + 2)) + (10(a + 2) + a) = 66 (10a + a + 2) + (10a + 20 + a) = 66 22a + 22 = 66 22a = 44 a = 2 b = a + 2 = 4
So, another such number is 24.
Hence, there are two such numbers: 24 and 42.
Systems of Linear Equations in Algebra
A system of linear equations is a collection of two or more linear equations involving the same set of variables. The general form of a linear equation in two variables x and y is:
ax + by = c
Where a, b, and c are constants, and a and b are not both zero. The solution to a linear equation is the set of values for the variables that make the equation true.
A system of linear equations involves multiple linear equations with the same variables. For example, a system of two linear equations in two variables x and y can be represented as:
ax + by = c dx + ey = f
A solution to a system of linear equations is a set of values for the variables that simultaneously satisfy all equations in the system. There are three possible scenarios for the solution of a system of linear equations:
 Consistent System: A system of equations that has at least one solution is called consistent.
 Inconsistent System: A system of equations that has no solution is called inconsistent.
 Dependent System: A system of equations that has infinitely many solutions is called dependent.
There are various methods to solve systems of linear equations, including:
 Graphical Method: Graphing each equation on the same coordinate plane and finding the point(s) of intersection, if any.
 Substitution Method: Solving one equation for one variable and substituting the expression into the other equation.
 Elimination Method: Adding or subtracting equations to eliminate one variable and then solving for the remaining variable.
 Matrix Method (or Gaussian Elimination): Representing the system of equations in matrix form and performing row operations to solve for the variables.
Each method has its advantages and is suitable for different situations. The choice of method often depends on the specific characteristics of the system of equations and personal preference.
The sum of a two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there  FAQs
1. What is a system of linear equations?
A system of linear equations involves multiple linear equations with the same variables.
2. What's the general form of a linear equation in two variables?
The general form is ax + by = c, where a, b, and c are constants and a and b are not both zero.
3. What's a solution to a linear equation?
A solution is a set of values for the variables that make the equation true.
Recent Updates
 Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboida...
 A house is on an 80,000 sq ft lot. About how many acres is the lot?
 Nik needs to estimate how many books will fit in a bin. Each book is 1’ tall, 0.5’ ...
 A bag contain 4 red, 5 blue and 3 green balls if two ball are drawn at random. What is ...
 A cubical block of side 0.5 m floats on water with 30 % of its volume under water. What...
 The length of a rectangular frame is 15 inches, and the width of the frame is 8 inches....
 A and B take part in a 100 m race. A runs at 5 km per hour. A gives B a start of 8 m a...
 What is the sum of First 35 Natural numbers?
 If January 1, 1996, was Monday, What day of the week was January 1, 1997?
 In a kilometer race, A beats B by 40 meters or by 5 seconds. What is the time taken by ...
 A bag contain 4 red, 5 blue and 3 green balls if two ball are drawn at random What is t...
 A Kiddie Pool has a diameter of 4 ft and height of 2 ft. About how many gallons are in ...
 In a college, 25 % of the boys and 10 % of the girls offer Mathematics. The girls const...
 If the sum of three consecutive numbers is 72. What is the largest number?
 The sum of three consecutive numbers is 72. What are the smallest of these numbers?