SOLUTION: Hi me again. I mostly having trouble with word problems *Math worst subject*, anyway, with this I started than got confused: *When the digits of a two-digit number are reversed,

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Question 129940This question is from textbook algebra
: Hi me again. I mostly having trouble with word problems *Math worst subject*, anyway, with this I started than got confused:
*When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original number?*
I am always thankful, or gonna be thankful when you guys help me, I always wanted help with this algebra book. Thankfully I got it.
Please and Thank You=)This question is from textbook algebra

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Let t=ten's digit of unknown number, u=unit's digit of unknown number


So our number is in this form

N=10%2At%2Bu


Now if the digits are reversed then our number becomes


M=10%2Au%2Bt


Since the new number is 9 more than the original number, this means

M=N%2B9


Also, because the sum of the digits of the original number is 11, we know that


t%2Bu=11


And solving for t, we get


t=11-u




M=N%2B9 Start with the third equation


10%2Au%2Bt=10%2At%2Bu%2B9 Plug in N=10%2At%2Bu and M=10%2Au%2Bt


10u%2B11-u=10%2811-u%29%2Bu%2B9 Plug in t=11-u. Notice how we now have one equation with one unknown



10u%2B11-u=110-10u%2Bu%2B9 Distribute


9u%2B11=110-10u%2Bu%2B9 Combine like terms on the left side


9u%2B11=-9u%2B119 Combine like terms on the right side


9u=-9u%2B119-11Subtract 11 from both sides


9u%2B9u=119-11 Add 9u to both sides


18u=119-11 Combine like terms on the left side


18u=108 Combine like terms on the right side


u=%28108%29%2F%2818%29 Divide both sides by 18 to isolate u



u=6 Divide

So we know that the unit's digit is 6



t=11-6 Plug in u=6


t=5 Subtract


So the ten's digit is 5




So the original number is 56 and the reversed number is 65