Alu (f. Lenny makes \( \$ 55,000 \) and is getting annual raises of \( \$ 2,500 \). Karl makes \( \$ 62,000 \), with annual raises of \( \$ 2,000 \). How many years will it take for Lenny and Karl to make the same salary? Define the variable: Y equation: Solve the equation in the space below. Show your work.

Let's define the variables: - Let \( Y \) be the number of years it will take for Lenny and Karl to make the same salary. We can set up an equation to represent the salaries of Lenny and Karl after \( Y \) years: - Lenny's salary after \( Y \) years: \( 55,000 + 2,500Y \) - Karl's salary after \( Y \) years: \( 62,000 + 2,000Y \) We want to find the value of \( Y \) when Lenny and Karl have the same salary, so we set the two expressions equal to each other: \[ 55,000 + 2,500Y = 62,000 + 2,000Y \] Now, we can solve this equation to find the value of \( Y \). Solve the equation by following steps: - step0: Solve for \(Y\): \(55000+2500Y=62000+2000Y\) - step1: Move the variable to the left side: \(55000+2500Y-2000Y=62000\) - step2: Subtract the terms: \(55000+500Y=62000\) - step3: Move the constant to the right side: \(500Y=62000-55000\) - step4: Subtract the numbers: \(500Y=7000\) - step5: Divide both sides: \(\frac{500Y}{500}=\frac{7000}{500}\) - step6: Divide the numbers: \(Y=14\) It will take 14 years for Lenny and Karl to make the same salary.