SOLUTION: The sum of the digits of a certain 2 digit number is 14. When the number is reversed it decreases by 18. What is the number. Need to qrite this in an equation form. I know the

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Question 559948: The sum of the digits of a certain 2 digit number is 14. When the number is reversed it decreases by 18. What is the number.
Need to qrite this in an equation form.
I know the answer by need the equation.
Thank you
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the digits of a certain 2 digit number is 14. When the number is reversed it decreases by 18. What is the number.
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Let t = the ten's place digit
Let u = the one's place digit
Given: t + u = 14 -> u = 14 - t
Let n = the number
The number can be represented as
n = 10t + u
And when the numbers are reversed the number is
n - 18 = 10u + t
Subsitute the value for u above in these two equations:
n = 10t + 14 - t = 9t + 14
n - 18 = 10(14-t) + t = 140 - 9t
Solve for n by adding the two equations together:
2n - 18 = 154
2n = 172
n = 86
Check:
8 + 6 = 14
86 - 68 = 18