Answer :
Answer:
The number such that the sum of its two digits is \(9\) and if \(27\) is added to the number, its digits are reversed.How to solveFormulate a system of equations based on the given information and solve it to find the required number.Step 1Define the variables.Let \(x\) represent the digit in the tens place.Let \(y\) represent the digit in the ones place.Step 2Formulate an equation given that the sum of the two digits is \(9\).\(x+y=9\)Step 3Formulate an equation given that if \(27\) is added to the number, its digits are reversed.When \(27\) is added to the number, the tens digit becomes \(y\) and the ones digit becomes \(x\).\(10y+x=10x+y+27\)Step 4Set up a system of equations:\(\begin{cases}x+y=9\\ 10y+x=10x+y+27\end{cases}\)Step 5Solve the system of equations.Simplify the equations and eliminate \(x\).\(\begin{cases}x+y=9\\ -9x+9y=27\end{cases}\)Divide both sides of the equation by \(9\).\(\begin{cases}x+y=9\\ -x+y=3\end{cases}\)Add the equations vertically to eliminate \(x\).\(2y=12\)Divide both sides of the equation by \(2\).\(y=6\)Substitute \(y=6\) into the equation that connects \(x\) and \(y\).\(x+y=9\)\(x+6=9\)Solve the equation for \(x\).\(x=3\)SolutionThe required number is \(36\)
Step-by-step explanation:
