SOLUTION: the sum of the digits of a two digit number is 12. the number is 13 times the tens digit. find the number. thanks for the help!

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Question 5479: the sum of the digits of a two digit number is 12. the number is 13 times the tens digit. find the number.
thanks for the help!
Answer by Abbey(339) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the digit in the 10's column
Let y be the digit in the one's column
So in order to find the value of the number we multiply the x by 10 and add it to the y (think about the number 23... it represents the value (2*10) + 3)
The sum of the two digits is 12:
x+y=12
we can rewrite this by subtracting x from both sides as:
y=12-x
the number is 13 times the 10's digit:
(10x+y=13x)
substitute the 12-x in for the y value and solve for x:
10x+(12-x)=13x
9x+12=13x
12=4x
3=x
If x=3, then 12-3 = 9, so y=9.
Our number is 39
check the answer:
3+9=12 (true)
39=13*3 (true)