
To solve: the system of two equations in two variables.

Answer to Problem 30P
The 2-digit number is 37.
Explanation of Solution
Given information:
The two digits in the numerator of a fraction are reversed in its denominator. If 1 is subtracted from both the numerator and the denominator, the value of the resulting fraction is
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:
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 |
This implies
The fraction whose numerator is the difference and whose denominator is the sum of the units and tens digit equals
Putting equation (ii) in (i) we get,
Put equation (iii) in (ii)
Tens | Units | Value | |
Original number |
Therefore, the 2-digit number is 37.
Chapter 9 Solutions
Algebra: Structure And Method, Book 1
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