In a two-digit number, the sum of the digits is 1/7 of the number itself. The digits in the tens place is three more than the digit in the unit place. Find the number.
Let the digit in tens place be `a` and digit in unit place be `b.` Now we have system of 2 equations with 2 unknowns.
Second equation is also substitution for `a` so we simply plug it into first equation.
Therefore, our number is 63.
The answer is 63.
Imagine the digits in units place is y and in ten's place is x. Then as per the question:
x = y +3 and x + y = 1/7 (10x + y)
Making substitution for x as y+ 3, we get
y + 3 + y = 1/7 (10. y + 10.3 +y)= 1/7 (11 y +30)
or 7. (2y +3) = 11y + 30
or 14 y + 21 = 11y + 30
or 3 y = 9 or y =3 and thus x = y + 3 = 6
and hence the number is 63.