The units digit of a two-digit number is 3 and seven times the sum of the digits is the number itself. Find the number.

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Solution

Let tens digit = x

Units digit = 3

$∴$ Number = 3 + 10x

According to the condition,

7 (x + 3) = 3 + 10x

7x + 21 = 3 + 10x

21 - 3 = 10x - 7x $\Rightarrow$ 3x = 18

$x = \frac{18}{3} = 6$

$∴$ Number = 3 + 10x

=3 + 10 $\times$ 6 = 3 + 60 = 63

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