SOLUTION: The ten's digit of two-digit number is 3 more than the units' digit. The number is 8 more than six times the sum of the digits. Find the number.

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Question 401585: The ten's digit of two-digit number is 3 more than the units' digit. The number is 8 more than six times the sum of the digits. Find the number.
Found 2 solutions by MathLover1, josmiceli:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


Let the ten digit be T and units digit U
The number will be 10T+%2B+U
The Ten's digit of a two-digit number is 3 more than the unit's digit.
T+=+3+%2B+U .....(1)
The number is 8 more than six times the sum of the digits:
10T+%2B+U+=+8+%2B+6%28T+%2B+U%29
10T+%2B+U+=+8+%2B+6T+%2B+6U
10T+%2B+U+-+6T+-+6U+=+8
4T+-+5U+=+8
substitute T+=+3+%2B+U
4%283+%2B+U%29+-+5U+=+8
12+%2B+4U+-5U+=8
-U+=+-4
U+=+4( UNIT'S DIGIT IS 4)
Since Ten's digit is 3 more than the unit's digit, it 7
Number is 74+

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the units digit a
Call the tens digit b
given:
(1) b+=+a+%2B+3
(2) 10%2Ab+%2B+a+=+6%2A%28a+%2B+b%29+%2B+8
----------------------------------
from (1), I get
(1) a+=+b+-+3
Substitute (1) into (2)
(2) 10%2Ab+%2B+a+=+6%2A%28a+%2B+b%29+%2B+8
(2) 10%2Ab+%2B+%28b+-+3%29+=+6%2A%28%28b+-+3%29+%2B+b%29+%2B+8
(2) 11b+-+3+=+12b+-+18+%2B+8
(2) b+=+7
And, from (1),
a+=+b+-+3
a+=+4
The number is 74
check answer:
(2) 10%2A7+%2B+4+=+6%2A%284+%2B+7%29+%2B+8
(2) 74+=+6%2A11+%2B+8
(2) +74+=+74
OK