Question

Dora makes $42,000 with a raise of $3,300 each year. Felicia earns

$62,000 with an annual raise of $1,800. How many years will it take
for Dora and Felicia to have the same salary?
Write an equation to represent this situation.

Answer 1

It will take 7 years for Dora and Felicia to have the same salary.

Step-by-step explanation:

Let "y" represent the number of years. The equations representing their salaries over time are as follows:

Dora's salary: $42,000 + $3,300y

Felicia's salary: $62,000 + $1,800y

To find when their salaries are equal, set the two expressions equal to each other:

$42,000 + $3,300y = $62,000 + $1,800y

Solving for "y":

$1,500y = $20,000

y = 13.33

Since we can't have a fraction of a year in this context, round up to the nearest whole number. Therefore, it will take 7 years for Dora and Felicia to have the same salary.

Answer 2

The equation representing the situation is 42000 + 3300x = 62000 + 1800x.

It will take approximately 13 years for Dora and Felicia to have the same salary.

Step-by-step explanation:

The equation representing the situation where Dora and Felicia will have the same salary after a certain number of years can be expressed as:

42000 + 3300x = 62000 + 1800x

Where:

• x represents the number of years.
• 42000 is Dora's initial salary.
• 3300x is the increase in Dora's salary over x years.
• 62000 is Felicia's initial salary.
• 1800x is the increase in Felicia's salary over x years.

This equation sets the total earnings of Dora after \(x\) years equal to the total earnings of Felicia after the same duration, allowing us to solve for x to determine the number of years it takes for their salaries to be equal.

To determine how many years it will take for Dora and Felicia to have the same salary, we can set up an equation based on their salaries and annual raises.

Let x represent the number of years.

• For Dora: Salary = $42,000 + ($3,300 * x)
• For Felicia: Salary = $62,000 + ($1,800 * x)

Setting their salaries equal to each other, we have: $42,000 + ($3,300 * x) = $62,000 + ($1,800 * x)

Simplifying the equation, we get:

$3,300 * x - $1,800 * x = $62,000 - $42,000

$1,500 * x = $20,000

x = $20,000 / $1,500

x = 13.33

Therefore, it will take approximately 13 years for Dora and Felicia to have the same salary.