Question

Emelina makes $42,000 with a raise of $3,800 each year. Lois earns $55,000 with an annual raise of $2,100. How many years will it take for Emelina and Lois to have the same salary?

Write an equation to represent this situation. Use 'x' as the variable.

Answer 1

To find when Emelina's and Lois's salaries will be the same, we solve the equation 42,000 + 3,800x = 55,000 + 2,100x, resulting in x equals roughly 7.647. Since we count full years, it will take 8 full years for their salaries to be equal.

Step-by-step explanation:

To determine when Emelina and Lois will have the same salary, we can set up an equation that represents the growth of their salaries over time. We'll let x be the number of years it takes for their salaries to be equal.

Emelina starts with a salary of $42,000 and gets a raise of $3,800 each year. Lois starts with a salary of $55,000 and gets a raise of $2,100 each year. We want to find the value of x when their salaries are the same.

The equation representing Emelina's salary after x years is:

Emelina's Salary = 42,000 + 3,800x

Similarly, the equation for Lois's salary after x years is:

Lois's Salary = 55,000 + 2,100x

To find when their salaries are equal, we set the two equations equal to each other and solve for x:

42,000 + 3,800x = 55,000 + 2,100x

3,800x - 2,100x = 55,000 - 42,000

1,700x = 13,000

x = 13,000 / 1,700

x = 7.647

Since x represents the number of full years, we can't have a fraction of a year. Therefore, it will take 8 full years for Emelina's salary to equal Lois's salary.