Questions: Lucas's age is 7 years more than twice Ethan's age. Lucas is 45 years old. How old is Ethan?

Solution Steps

To solve the problem, we need to set up an equation based on the information given. We know that Lucas's age is 7 years more than twice Ethan's age, and Lucas is 45 years old. We can represent Ethan's age as a variable, say \( E \). The equation will be: \( 2E + 7 = 45 \). We will solve this equation to find Ethan's age.

We know that Lucas's age is 7 years more than twice Ethan's age. We can express this relationship mathematically as: \[ L = 2E + 7 \] where \( L \) is Lucas's age and \( E \) is Ethan's age. Given that \( L = 45 \), we can substitute this value into the equation: \[ 45 = 2E + 7 \]

To find Ethan's age, we will isolate \( E \) in the equation. First, we subtract 7 from both sides: \[ 45 - 7 = 2E \] This simplifies to: \[ 38 = 2E \] Next, we divide both sides by 2: \[ E = \frac{38}{2} = 19 \]

Final Answer