SOLUTION: The ten's digit of a two digit number is 3 more than the unit's digit. The number is eight more than six times the sum of the digits. Find the number.

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Question 197870: The ten's digit of a two digit number is 3 more than the unit's digit. The number is eight more than six times the sum of the digits. Find the number.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the tens digit a
Call the units digit b
The number is 10a+%2B+b
given:
(1) a+=+b+%2B+3
(2) 10a+%2B+b+=+6%2A%28a+%2B+b%29+%2B+8
Substitute (1) in (2)
(2) 10%2A%28b+%2B+3%29+%2B+b+=+6%2A%28b+%2B+3+%2B+b%29+%2B+8
10b+%2B+30+%2B+b+=+6b+%2B+18+%2B+6b+%2B+8
11b+%2B+30+=+12b+%2B+26
b+=+4
And, from (1)
a+=+4+%2B+3
a+=+7
The number is 74
check answer:
(2) 10a+%2B+b+=+6%2A%28a+%2B+b%29+%2B+8
10%2A7+%2B+4+=+6%2A%287+%2B+4%29+%2B+8
74+=+6%2A11+%2B+8
74+=+74