|
Question 387243: WHAT NUMBER AM I I AM A PALIDROME THE SUM OF MY HUNDREDS DIGIT 3 TIMES MY TENS DIGIT AND MY ONES DIGIT IS 24. THE SUM OF MY HUNDREDS DIGIT MY TENS DIGIT AND 3 TIMES MY ONE DIGIT IS 32. THE SUM OF 3 TIMES MY HUNDREDS DIGIT MY TENS DIGIT AND MY ONES DIGIT IS 34. I AM DIVISIBLE BY 9. I AM AN ODD NUMBER. I AM GREATER THAN 700000. MY TEN THOUSANDS DIGIT IS 3. AND M THOUSANDS DIGIT IS 8.
Found 2 solutions by ankor@dixie-net.com, robertb:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A PALIDROME
THE SUM OF MY HUNDREDS DIGIT 3 TIMES MY TENS DIGIT AND MY ONES DIGIT IS 24. THE SUM OF MY HUNDREDS DIGIT MY TENS DIGIT AND 3 TIMES MY ONE DIGIT IS 32. THE SUM OF 3 TIMES MY HUNDREDS DIGIT MY TENS DIGIT AND MY ONES DIGIT IS 34. I AM DIVISIBLE BY 9. I AM AN ODD NUMBER. I AM GREATER THAN 700,000. MY TEN THOUSANDS DIGIT IS 3. AND MY THOUSANDS DIGIT IS 8.
:
Let:
a = units
b = 10's
c = 100's
:
"THE SUM OF MY HUNDREDS DIGIT 3 TIMES MY TENS DIGIT AND MY ONES DIGIT IS 24."
c + 3b + a = 24
:
MY TEN THOUSANDS DIGIT IS 3. AND MY THOUSANDS DIGIT IS 8.
Since it is a palidrome we can write it:
_ 3 8 8 3 _
therefore
c = 8
b = 3
:
Find a
c + 3b + a = 24
8 + 3(3) + a = 24
17 + a = 24
a = 24 - 17
a = 7
:
7 3 8 8 3 7 is the number, odd and divisable 9
Answer by robertb(5830)  (Show Source):
You can put this solution on YOUR website! From the opening sentence , we get the linear system:
h + 3t + u = 24,
h + t + 3u = 32,
3h + t + u = 34.
This system has the solution h =8, t = 3, and u = 7. (You can check!)
The problem says the ten-thousands digit is 3, and the thousands digit is 8. Since it is a palindrome, the hundred-thousands digit should also be 7. The proposed number is 738,837.
Check: The number is divisible by 9: 738,837 / 9 = 82,093.
It is an odd number, and the number is greater than 700,000.
|
|
|
| |
