the sum of the digits of a three digit number is 14.
the tens digits exceeds twice the hundred digit by one.
If 3 were added to the number,
the units and hundreds digit would be the same.
find the number.
solve
H = hundred digit
t in ten digit
u in unit digit
sum of the digits of 3 digit number is 14: H+t+u=14
ten digits exceeds twice the hundred digit by one: t-2h+1
if 3 were added to the number, the units and hundred digit would be the same: u-2h+1+3 = h-2h+1+3
therefore, u-2h+4+h-4=0
u-h=0
i don't know what is next step, but the answer given for this problem is 491. i don't know how to get this answer 491.
could some one please help? Thank you.
please help i get stuck on this problem
To find the number, we need to solve the system of equations based on the given information:
1) The sum of the digits of a three-digit number is 14: H + t + u = 14
2) The tens digit exceeds twice the hundred digit by one: t = 2H + 1
3) If 3 is added to the number, the units and hundreds digits would be the same: u + 3 = H + 3
Simplifying equation (2) and (3), we have:
t - 2H = 1
u = H
Substituting equation (2) and (3) in equation (1), we get:
H + (2H + 1) + H = 14
4H + 1 = 14
4H = 13
H = 13/4
Since a three-digit number cannot have a fraction as the hundreds digit, we can conclude that there is no solution to the problem as given. The answer provided (491) does not satisfy the given conditions.