SOLUTION: A two-digit number is 2 more than 8 times the sum of its digits. Find the number if its tens digit is 6 more than its unit digit.

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Question 1110921: A two-digit number is 2 more than 8 times the sum of its digits. Find the number if its tens digit is 6 more than its unit digit.
Answer by ikleyn(52785) About Me  (Show Source):
You can put this solution on YOUR website!
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Answer.  82.

Solution 

Let the decimal form of the number is "ab".


Then 

10a + b = 2 + 8*(a+b)      ("A two-digit number is 2 more than 8 times the sum of its digits")

10a + b = 2 + 8a + 8b,

2a = 2 + 7b.      (1)



Also,

a = 6 + b          (2)      ("tens digit is 6 more than unit digit")



Substitute (2) into (1). You will get

12 + 2b = 2 + 7b,

10 = 5b  ====>  b = 2.


Then a = b+6 = 2 + 6 = 8,   and you get the answer.