SOLUTION: the sum of a two digit number is 9. the number is 12 times the tens digit. find the number

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Question 547683: the sum of a two digit number is 9. the number is 12 times the tens digit. find the number
Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
So I will let a represent the tens digit of the number I am looking for and b represent the ones digit. (so my number will end up in the form ab).
Since the sum of the two digits is 9 this means:
a%2Bb=9 (1)
Also, since the number is 12 times the tens digit, this means:
a%2A12=ab ((note: ab is the whole number NOT a*b))
This can be rewritten as
10%2Aa%2B2%2Aa=10%2Aa%2Bb
so
2%2Aa=b (2)
Substituting (2) into (1) we get:
a%2B2%2Aa=9
3a=9
a=3
And so b=2%2A3=6

So our number is 36.
HOpefully this helps, let me know if you are still unsure:)