<PRE><B>Question 651576</B>
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
{{{(100(n+4) + 10n + (n+2))/2(3n+6)}}} = {{{(100n + 400 + 10n + n + 2)/(6n+12)}}} = {{{(111n+402)/(6n+12)}}} = {{{(3(37n+134))/(3(2n+4))}}}
Cancel 3
{{{((37n+134))/((2n+4))}}} = {{{423/18}}}
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)
{{{846/2(18)}}} = 846/36 reduces to 423/18
</PRE>