The sum of two numbers is ##69## and their difference is ##23##. What is the smaller number?

##23## is the smaller number.

Let the first number be ##x## and the second number be ##y##. In this case, the simultaneous equations would be: ##x+y=69## ##x-y=23##

Let's label the first equation as equation 1 and the second one as equation 2. Now, we want to find only one unknown at a time, so we'll use substitution to get only one unknown at a time. Let's do ##y## first. From equation 2,

##x=23+y## Let this be equation 3. Now, we shall substitute the ##x## in equation 1 with Equation 3. ##=> (23+y)+y=69## ##2y=69-23## ##2y=46## ##y=23##

Now that we have one unknown, let's solve for the other by substituting this value of ##y## into equation 1. ##x+23=69## ##x=46##

##:.##the two numbers are ##46## and ##23##, with ##23## being the smaller number.