SOLUTION: A two digit number and the reulting number when the digits are reversed are in the ratio 2:9.If the sum of the digits is 9,Find the original number.

Algebra ->  Inequalities -> SOLUTION: A two digit number and the reulting number when the digits are reversed are in the ratio 2:9.If the sum of the digits is 9,Find the original number.      Log On


   

Question 729530: A two digit number and the reulting number when the digits are reversed are in the ratio 2:9.If the sum of the digits is 9,Find the original number.
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Let this two digit number be 10%2Ax%2B1%2Ay.
The digit reversal of the number would be 10%2Ay%2B1%2Ax.

The ratio as stated gives the proportion, highlight%28%2810x%2B1%29%2F%28x%2B10y%29=2%2F9%29.
The sum of the digits being 9 means highlight%28x%2By=9%29.

Now that the conversion into symbolism and equations has been made, most of the problem, the harder part, is solved. Merely solve the resulting system for x and y.