The tens digit in a two digit number is 4 greater than one’s digit. If we interchange the digits in the number, we obtain a new number that, when added to the original number, results in the sum of 88. Find this number

The original digit is 62

Step-by-step explanation:

Let the Tens be represented with T

Let the Units be represented with U

Given:

Unknown Two digit number

Required:

Determine the number

Since, it's a two digit number, then the number can be represented as;

From the first sentence, we have that;

Interchanging the digit, we have the new digit to be

So;

Collect Like Terms

Divide through by 11

Recall that

becomes

Collect like terms

Divide both sides by 2

Substitute 2 for U in

Recall that the original digit is

Substitute 6 for T and 2 for U

Hence, the original digit is 62