This is the last part of the series on How to Solve Digit Problems in Algebra. In this post, we are going to solve another digit problem involving 3-digit numbers just like in the previous post.
The sum of the digits of a 3-digit number is 10. The hundreds digit is 3 more than the tens digits. If 198 is subtracted from the number, then the digits are reversed. What is the number?
Solution and Explanation
Since this is already the fifth part of the series, we won’t be as detailed as the previous parts.
= hundreds digit of the number
= tens digit of the number
= units (or ones) digit of the number.
The first sentence says the sum of the digits of the number is 10. So,
–> (Equation 1).
The hundreds digit is 3 more than the tens digit.
–> (Equation 2).
If is subtracted from the number, the digits are reversed.
Simplifying the preceding equation, we have
Dividing both sides by , we have
–> (Equation 3).
We can eliminate by adding Equation 1 and Equation 3.
We substitute from Equation 2 to in (*)
Substituting the value of in Equation 2,
Substituting the values of and in Equation 1,
So, the hundreds digit is 5, tens digit is 2, and ones digit is 3. Therefore, the number is 523.
If we check with the conditions above, we have
(1) The sum of the digits is 10. That is, 5 + 2 + 3 = 10
(2) The hundreds digit is 3 more than the tens digit. The hundred digit is 5 is 3 more than 2
(3) If 198 is subtracted from the number, the digits are reversed. That is, 523 – 198 = 325.