To solve: the problems about three-digit numbers.
Answer to Problem 26P
The 3-digit number is 342.
Explanation of Solution
Given information:
The sum of the three digits is 9. The tens digit is 1 more than the hundreds digit . When the digits are reversed, the new number is 99 less than the original number.
Formula used:
Digit problems are based on our decimal system of numeration.
Step1. The problem asks for the original number.
Step2. Let h = the hundreds digit of the original number.
Let t = the tens digit of the original number.
Let u = the units digit of the original number.
Step3. Use the facts of the problem to write two equations.
Step4. Solve the equations.
Calculation:
Consider ,
Let h = the hundreds digit of the original number.
Let t = the tens digit of the original number.
Let u = the units digit of the original number.
Hundreds | Tens | Units | Value | |
Original number |
According to the question:-
Since , tens digit is 1 more than the hundreds digit
Therefore,
Hundreds | Tens | Units | Value | |
Original number | ||||
Number reversed | u | h |
Now,
Substituting equation (vi) in equation (iii)
Putting value of h in equation (iv) we have,
Putting value of h in equation (ii) we have,
Hundreds | Tens | Units | Value | |
Original number |
The 3-digit number is 342.
Chapter 9 Solutions
Algebra: Structure And Method, Book 1
Additional Math Textbook Solutions
College Algebra with Modeling & Visualization (5th Edition)
Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)
Algebra and Trigonometry (6th Edition)
Linear Algebra and Its Applications (5th Edition)
College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education