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
Algebra.Com
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) (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
= = =
Cancel 3
=
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)
= 846/36 reduces to 423/18
RELATED QUESTIONS
The digits of the three digit number are three consecutive even integers. The middle... (answered by stanbon)
A three digit number is equal to 17 times the sum of its digit
If 198 is added to the... (answered by Alan3354)
A three digit number is equal to 17 times the sum of its digit
If 198 is added to the... (answered by stanbon)
a three digit number is equal to17 times the sum of its digits.
if 198 is added to the... (answered by Edwin McCravy)
The sum of the digits of a three digit number is 17. The middle digit is two more than... (answered by ankor@dixie-net.com)
The sum of the digits of a three digit number is 17. The middle digit is two more than... (answered by mananth)
6) If twenty seven is added to a two digit #, the original # will be reversed. The number (answered by solver91311)
The sum of three digits is 5. The first and last digits are the same. If the middle digit (answered by ankor@dixie-net.com)
the sum of the last two digits of a three digit counting number is 7. the sum of the... (answered by solver91311,oscargut)