Question

The sum of the two digits of a number is 16. The number formed by reversing the digits is 18 more than the original number. Determine the original number. Let t = the tens digit, u = the units digit, and u + t = 16. Which of the following equations would complete the system

Answer 1

Let \(x\) be the number. Since it has two digits, we can write it as
\[x=10a+b\]
where \(a\) is the digit in the tens place, and \(b\) the digit in the ones place.

We know that \(a+b=16\). If we reverse the digits, so that we get \(10b+a\) as our new number, we have that this new number is 18 more than \(x\):
\[10b+a=18+10a+b\]
You have a system of two equations with two unknowns. Go ahead and solve for \(a\) and \(b\).