The units' digit of a two-digit number is 4 less than 3...

Name: Problem 1212, Chapter 42: Algebra and Trigonometry
Uploaded: 2020-07-31T18:20:32-08:00
Duration: 2 min 9 s
Channel: Ankit Gupta
Description: The units' digit of a two-digit number is 4 less than 3 times the tens' digit. If the digits are reversed, a new number is formed which is 12 less than twice the original number. Find the number.

The units' digit of a two-digit number is 4 less than 3 times the tens' digit. If the digits are reversed, a new number is formed which is 12 less than twice the original number. Find the number.

Key Concepts

Two-Digit Number Representation

This concept involves expressing a two-digit number in terms of its tens and units digits, typically represented as 10t + u where t is the tens digit and u is the units digit. This representation leverages the base-10 place value system and is essential for manipulating and analyzing the number algebraically.

Digit Reversal

Digit reversal is the process of swapping the positions of the tens and units digits in a two-digit number. When a number represented as 10t + u is reversed, it becomes 10u + t. This concept is often used in problems involving symmetry or where the relationship between the original number and its reversed version must be explored.

Translating Verbal Conditions into Equations

This concept is about converting the problem's worded statements into algebraic equations. It involves identifying relationships and constraints provided in the problem and expressing these relationships using variables and arithmetic operations. This skill is crucial in bridging the gap between language and mathematics.

Solving Systems of Linear Equations

Once the verbal conditions have been translated into equations, solving them often requires handling a system of linear equations. This process involves determining the values of the variables that satisfy all the given equations simultaneously, various strategies include substitution, elimination, or matrix methods.

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