A number is such that its tens digit is twice its units digit. Prove that the number itself must be seven times the sum of its digits.

x - ten digit y - unit digit
x = 2 y 10 x + y = 7 ( x + y ) 10 ⋅ 2 y + y = 7 ( 2 y + y ) 20 y + y = 14 y + 7 y 21 y = 21 y ⇒ y ∈ \mathb R ⇒ x ∈ \mathb R
So it's true.

Answered by konrad509 | 2024-06-10

A number where the tens digit is twice the units digit must equal seven times the sum of its digits. This is proven by substituting the digits into the equations for the number and the sum. The equality holds true for all values of the digits as shown in the calculations.
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Answered by konrad509 | 2024-12-26