SOLUTION: Can you please help me solve the following word problem and the formula used to solve it? A two digit number is 6 times the sum of it digits. Two times the units digit is three

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Question 170484: Can you please help me solve the following word problem and the formula used to solve it?
A two digit number is 6 times the sum of it digits. Two times the units digit is three more than the tens digit. Find the units. The multiple choice answers are: a) 2 b) 3 c) 4 d) 5 e)6
thank you for your help, Phillip
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
sure!!!!!!
your looking for a two digit number lets call the tens digit a and ones unit be b.
so 10a+1b=6(a+b)
and 2b=a+3---->a=2b-3
:
10a+b=6a+6b--->4a-5b=0
.............. a-2b=-3 multiply bottom equation by -4 to eliminate a terms
:
8b-5b=12
:
highlight%28b=4%29 which is the units digit
highlight%28a=2%284%29-3=5%29 which is the tens unit
so our number is 54