SOLUTION: if a certain two digit number is divided by the sum of its digits, the quotient is 3. if the digits are reversed, the new number is 9 less then three times the original number. fin

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Question 226573: if a certain two digit number is divided by the sum of its digits, the quotient is 3. if the digits are reversed, the new number is 9 less then three times the original number. find the original number.
I think i have one of the equations: I used Z as my new number and X as the original number. Z=3X-9
could you help me solve this using a set of system of equations?
Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = original number and y = reversed number

Any two digit number is of the form x=10t%2Bu. Ex: 21=10*2+1 (think of t is the tens digit and u as the units/ones digit)


So x=10t%2Bu and y=10u%2Bt (just swap t and u)


The statement "if a certain two digit number is divided by the sum of its digits, the quotient is 3" translates to x%2F%28t%2Bu%29=3 (because t+u is the sum of the digits). Plug in x=10t%2Bu to get %2810t%2Bu%29%2F%28t%2Bu%29=3. So this is our first equation.


"if the digits are reversed, the new number is 9 less then three times the original number" translates to y=3x-9. Plug in x=10t%2Bu and y=10u%2Bt to get 10u%2Bt=3%2810t%2Bu%29-9. This is the second equation.


So you now have the system system%28%2810t%2Bu%29%2F%28t%2Bu%29=3%2C10u%2Bt=3%2810t%2Bu%29-9%29


Because you have two equations with two unknowns, you can find the unique solution which means you can find t and u. I'll let you do that. Let me know if you still need help.