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In another lesson, we have considered some examples of Digit Word Problems.

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

Related Topics:

Different types of Digit Word Problems

More Algebra Word Problems

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

**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 |

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

10*x* + *t = *10*t* + *x *– 45

10*x* – *x* + *t* = 10*t* – 45 *(–x to both sides)*

10*x* – *x* = 10*t* – *t* – 45 *(– t to both sides)*

10*x* – *x* + 45 = 10*t* – *t (+ 45 to both sides)*

10*t* – *t = *10*x* – *x *+ 45

9*t* = 9*x* + 45 (equation 2)

Substitute equation 1 into equation 2

9*t* = 9(11 – *t*) + 45

9*t* = 99 – 9*t* + 45

Isolate variable *t*

9*t* + 9*t* = 99 + 45

18*t* = 144

The ten’s digit is 8. The one’s digit is 11 – 8 = 3

Systems of Equations - Reversing Digits Word Problem #1

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?

Systems of Equations - Reversing Digits Word Problem #2

Reversing digits word problem.

Problem: The sum of two digits of a 2-digit number is 13. Reversing the digits increase the number by 45. What is the number?

Problem: The sum of two digits of a 2-digit number is 5. When the digits are reversed, the number is 9 greater than the original number. What is the original number?

Problem: The sum of two digits of a 2-digit number is 9. When the digits are reversed, the number is 9 less than three times the original. What is the original number?

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