The sum of the digits of a two-digit number is 9 . If the digits are reversed, the new number is

step 1 The sum of the digits of a two -digit number is nine. If the digits are reversed, the new number

The sum of the digits of a two-digit number is 9 . If the...

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Key Concepts

Reversal of Digits

Reversing the digits of a two-digit number changes the number's value, which can be represented as 10b + a for a number originally written as 10a + b. This concept is crucial when problems involve comparisons between a number and its reversed form, as it allows the creation of an equation that captures the effect of the reversal.

System of Linear Equations

By translating the problem's conditions into algebraic equations, one creates a system of linear equations that models the situation. Solving these systems using substitution or elimination methods is a key technique in algebra that provides a structured approach to finding unknown quantities.

Place Value Representation

In two-digit numbers, each digit occupies a specific place value: the tens place and the ones place. Representing a two-digit number as 10a + b, where a is the tens digit and b is the ones digit, is fundamental in algebraic problem-solving as it allows the conversion of verbal statements into mathematical expressions.

Digit Sum Constraint

Many problems involve a constraint on the sum of the digits of a number. Recognizing that the sum of the digits can be expressed as a simple equation (a + b = a specific value) is important for formulating and solving problems related to number properties and digit relationships within a number.

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