SOLUTION: the digits of a three- digit number are three consecutive even integers. The middle digit is the least and the first digit is the greatest. If the number is divided by twice the su

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Question 651576: the digits of a three- digit number are three consecutive even integers. The middle digit is the least and the first digit is the greatest. If the number is divided by twice the sum of its digits, the quotient is 423/18. Find the number. pls really need ur help
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
the digits of a three-digit number are three consecutive even integer
:
The middle digit is the least and the first digit is the greatest.
Let n = the middle digit
then
(n+4) = the greatest
and
(n+2) = the next greatest
:
The sum of the three digits:
n + (n+2) + (n+4) = (3n+6)
:
If the number is divided by twice the sum of its digits, the quotient is 423/18
%28100%28n%2B4%29+%2B+10n+%2B+%28n%2B2%29%29%2F2%283n%2B6%29 = %28100n+%2B+400+%2B+10n+%2B+n+%2B+2%29%2F%286n%2B12%29 = %28111n%2B402%29%2F%286n%2B12%29 = %283%2837n%2B134%29%29%2F%283%282n%2B4%29%29
Cancel 3
%28%2837n%2B134%29%29%2F%28%282n%2B4%29%29 = 423%2F18
Cross multiply
423(2n+4) = 18(37n + 134)
846n + 1692 = 666n + 2412
846n - 666n = 2412 - 1692
180n = 720
n = 720/180
n = 4 is the middle digit of the number
then
4 + 4 = 8 is the 1st digit
and
4 + 2 = 6 is 3rd digit
:
846 is the number
:
:
Check this; (number over twice the sum of the digits)
846%2F2%2818%29 = 846/36 reduces to 423/18