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
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Question 287025: 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
:
Let the three digits be, x, y, z
then
100x + 10y + z = the three digit number
:
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
:
"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
:
In the equation 72x = 18y + 27z, replace x with (z-3) and y with .5z, find z:
72(z-3) = 18(.5z) + 27z
72z - 216 = 9z + 27z
72z - 216 = 36z
72z - 36z = 216
36z = 216
z =
z = 6
then
x = 6 - 3
z = 3
and
y = .5(6)
y = 3
:
336 is the 3 digit number
:
:
See if that's true in 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
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