i am a 5 digit palindromic number. My third digit is 5 more than my fifth digit , my fourth digit is 2 times greater than my first digit. The sum of my digit is 14 What number am i?
the number is abcba
c = a+5
b = 2a
2a+2b+c = 14
(a,b,c) = (1,3,6)
the number is 13631
Note the possibly confusing "2 times greater" which means "3 times as much".
Instead of using algebra, if we just start guessing, then
if we let a=1, that makes c=6 and 2a+c=8, so dividing that up equally into 2b, b=3.
To find the number that meets these requirements, let's break down the clues:
1. The number is palindromic, which means it reads the same forwards and backwards.
2. The sum of the digits is 14.
3. The third digit is 5 more than the fifth digit.
4. The fourth digit is 2 times greater than the first digit.
To solve this, we can go through the possible values for the first digit (from 1 to 9) and deduce the rest of the digits based on the given clues.
Let's try all the possibilities one by one:
1. If the first digit is 1:
- The fourth digit would be 2 times greater, so it would be 2.
- The sum of the first, second, and fourth digits is 1 + a + 2 = 14 - (1 + a) (where "a" represents the second digit).
- Simplifying, we get: 3a = 11 - a.
- Solving for "a," we find that a = 2. However, this violates the condition that the third digit is 5 more than the fifth digit, so this is not a valid possibility.
2. If the first digit is 2:
- The fourth digit would be 2 times greater, so it would be 4.
- The sum of the first, second, and fourth digits is 2 + 3 + 4 = 9.
- The sum of the third and fifth digits is 14 - 9 = 5.
- Since the third digit is 5 more than the fifth digit, the third digit must be 4 and the fifth digit must be -1 (which is not possible since it must be a positive single-digit number).
3. If the first digit is 3:
- The fourth digit would be 2 times greater, so it would be 6.
- The sum of the first, second, and fourth digits is 3 + a + 6 = 14 - (3 + a) (where "a" represents the second digit).
- Simplifying, we get: 2a = 5 - a.
- Solving for "a," we find that a = 1.
- The third digit is 5 more than the fifth digit, so the third digit is 6 and the fifth digit is 1.
- Therefore, the number is 31613.