Concept explainers
To solve: the problems about two-digit numbers.
Answer to Problem 10P
The number is 71.
Explanation of Solution
Given information:
The sum of the digits of a two-digit is one third of the number. The units digit is 5 more than the tens digit.
Formula used:
Digit problems are based on our decimal system of numeration.
Step1. The problem asks for the original number.
Step2. 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 t = the tens digit of the original number.
Let u = the units digit of the original number.
Tens | Units | Value | |
Original number | t | u | |
Number reversed | u | t |
According to the question,
Also,
Let u = the units digit of the original number.
Let t = the tens digit of the original number.
Therefore,
Substituting equation (ii) in (i) we get,
Putting value of u in equation (ii) we get,
Thus , the 2-digit number is 71.
Chapter 9 Solutions
Algebra: Structure And Method, Book 1
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