SOLUTION: A three digit number divisible by ten has a hndreds digit that is one less than its tens digit.The number is 52 times the sum of the digits.Find the digits.

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Question 659776: A three digit number divisible by ten has a hndreds digit that is one less than its tens digit.The number is 52 times the sum of the digits.Find the digits.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
a three-digit number, which is divisible by 10,
has a hundreds digit that is one+less than its tens digit
the number also is 52+times the sum of its digits
solution:
Since it is divisible by 10, let the number be
100a+%2B+10b............1 ...where a+=+b+-+1
100a+%2B+10b+=+52%28a%2Bb%29.......2
________________________________________
Use substitution to solve for "b":
100%28b-1%29+%2B+10b+=+52%28b-1%2Bb%29
100b+-+100+%2B+10b+=+104b+-+52
6b+=+48
highlight%28b+=+8%29
now, solve for "a":
a+=+8-1
highlight%28a+=+7%29

so, the number is 100%2A7+%2B+8%2A10+=+highlight%28780%29