1. **State the problem:** We are given two equations to solve for the number $x$. Equation 1: $3x = 45$ Equation 2: The difference between 3 times a number and 5 is sixteen, which translates to $3x - 5 = 16$ 2. **Solve Equation 1:** $$3x = 45$$ Divide both sides by 3: $$\cancel{3}x = \cancel{3}15$$ $$x = 15$$ 3. **Solve Equation 2:** $$3x - 5 = 16$$ Add 5 to both sides: $$3x - 5 + 5 = 16 + 5$$ $$3x = 21$$ Divide both sides by 3: $$\cancel{3}x = \cancel{3}7$$ $$x = 7$$ 4. **Interpretation:** The first equation gives $x=15$, the second gives $x=7$. These are two separate problems. **Final answers:** - For $3x=45$, $x=15$ - For $3x - 5=16$, $x=7$