Math Problem Statement
If a two digit number is divided by the sum of the digits the quotient is 9. But the number obtained by reducing the digits at the tens place by four times the digits at the units place leaves the remainder 5 when divided by the sum of the digits of the original number find the original number
Solution
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Math Problem Analysis
Mathematical Concepts
Algebra
Number Theory
Modular Arithmetic
Formulas
General form of a two-digit number: 10x + y
Condition 1: (10x + y) / (x + y) = 9
Condition 2: (10(x - 4y) + y) mod (x + y) = 5
Theorems
Properties of Modulo Operation
Basic Algebraic Manipulation
Suitable Grade Level
Grades 8-10
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