OML Search

Digit Word Problems - Interchanging of digits




 

In previous lessons, we have considered some examples of Digit Word Problems.

In these lessons, we will consider examples of Digit Word Problems that involve the interchanging of digits.

Related Topics: Different types of Digit Word Problems

Convert Digits to Number

If the problem involves interchanging of the digits in the integer then you would need to convert from the digits to numbers and vice versa. To convert the digits to numbers, we need to multiply with the digit with the place value of the digit.

For example, the value of the number formed by the digit 4 in the ten’s place and the digit 3 in the one’s place is 4 × 10 + 3 × 1

This type of digit problems is shown in the following example

Interchanging Of Digits Problems

Example:

The sum of the digits of a two-digit number is 11. If we interchange the digits then the new number formed is 45 less than the original. Find the original number.

Solution:

Step 1:
Assign variables
Let x = one’s digit and t = ten’s digit

Sentence: The sum of the digits of a two-digit number is 11.
x + t = 11

Isolate variable x
x = 11 – t             (equation 1)

Step 2:
Convert digits to number
Original number = t × 10 + x
Interchanged number = x × 10 + t
Sentence: If we interchange the digits then the new number formed is 45 less than the original.
Interchanged = Original – 45
x × 10 + t = t × 10 + x – 45
10x + t = 10t + x – 45
10xx + t = 10t – 45 (–x to both sides)
10xx = 10tt – 45 (– t to both sides)
10xx + 45 = 10tt (+ 45 to both sides)
10tt = 10xx + 45 (Rewrite equation with t on the left hand side)

Combine like terms
10tt = 10xx + 45
9t = 9x + 45            (equation 2)

Substitute equation 1 into equation 2
9t = 9(11 – t) + 45
9t = 99 – 9t + 45

Isolate variable t
9t + 9t = 99 + 45
18t = 144
t=144/18=8
The ten’s digit is 8. The one’s digit is 11 – 8 = 3

Answer: The number is 83.




Videos

How to use Systems of Equations to solve Reversing Digits Word Problem?
Reversing digits word problem
Problem: The sum of two digits of a 2-digit number is 11. Reversing the digits increase the number by 45. What is the number?
Example: The sum of two digits of a 2-digit number is 13. Reversing the digits increase the number by 45. What is the number?


 

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


OML Search


We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.


[?] Subscribe To This Site

XML RSS
follow us in feedly
Add to My Yahoo!
Add to My MSN
Subscribe with Bloglines