Answer:
There are 3 three-digit palindromes satisfy the property.
242
, 313 and 404
Step-by-step explanation:
Consider the provided information.
It is given that the sum of three things -- the hundreds digit, the units digit, and the product of the units and tens digits -- is eight more than the tens digit.
Let the number is "aba" (last and first digit will be same, As it is palindromes)
Then we have:
a + a + ba = b + 8
2a + ba - b = 8
Substitute a = 1 in 2a + ba - b = 8
2 + b - b = 8
2 ≠ 8 so 'a" can't be 1.
Substitute a = 2 in 2a + ba - b = 8
4 + 2b - b = 8
b = 8-
4
b = 4
So, the first number is: 242
Substitute a = 3 in 2a + ba - b = 8
6 + 3b - b = 8
2b = 2
b = 1
So, the second number is: 313
Substitute a = 4 in 2a + ba - b = 8
8 + 4b - b = 8
3b = 8-8
b = 0
So, the third number is: 404
Substitute a = 5 in 2a + ba - b = 8
10 + 5b - b = 8
4b = -2
b should be whole number so no other numbers are possible.
Hence, there are 3 three-digit palindromes satisfy the property.
242
, 313 and 404
