SOLUTION: A three-digit number is 28 times the sum of its digits. The units digit is twice the tens digit and 3 more than the hundreds digit. find the number.
Algebra ->
Customizable Word Problem Solvers
-> Numbers
-> SOLUTION: A three-digit number is 28 times the sum of its digits. The units digit is twice the tens digit and 3 more than the hundreds digit. find the number.
Log On
Question 140573: A three-digit number is 28 times the sum of its digits. The units digit is twice the tens digit and 3 more than the hundreds digit. find the number. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A three-digit number is 28 times the sum of its digits. The units digit is twice the tens digit and 3 more than the hundreds digit. Find the number.
:
x = 100's digit
y = 10's digit
z = units
:
write an equation for each statement:
"A three-digit number is 28 times the sum of its digits."
100x + 10y + z = 28(x+y+z)
:
100x + 10y + z = 28x + 28y + 28z
100x - 28x = 28y - 10y + 28z - z
72x = 18y + 27z
Simplify, divide equation by 9
8x = 2y + 3z
:
"The units digit is twice the tens digit"
z = 2y
or
y = .5z
:
" and 3 more than the hundreds digit."
z = x + 3
or
x = (z - 3)
:
find the number.
Using the equation: 8x = 2y + 3z, substitute .5z for y and (z-3) for x
8(z-3) = 2(.5z) + 3z
8z - 24 = z + 3z
8z - 24 = 4z
8z - 4z = +24
4z = 24
z =
z = 6
:
Using the substitution equation find x and y:
x = 6 -3
x = 3
:
y = .5(6)
y = 3
:
Our number 336
:
:
Check the solution using the statement
"A three-digit number is 28 times the sum of its digits."
336 = 28(3+3+6)
336 = 28(12); confirms our solution
