Question

Anissa has job offers at two companies. One company offers a starting salary of $60,000 with a raise of $2,000 each year. The other company offers a starting salary of $54,000 with a raise of $3,000 each year. In how many years would Anissa's salary be the same with both companies? What will be the salary?

Option 1: 3 years, $66,000
Option 2: 4 years, $66,000
Option 3: 5 years, $60,000
Option 4: 6 years, $60,000

Answer 1

Anissa's salary will be the same at both companies after 6 years, and the salary at that point will be $60,000.

Step-by-step explanation:

To find the number of years when Anissa's salary will be the same at both companies, we need to set up an equation. Let y represent the number of years, s1 represent the starting salary at the first company ($60,000), s2 represent the starting salary at the second company ($54,000), and r1 and r2 represent the annual raises at the first and second companies, respectively. The equation is:

s1 + (y * r1) = s2 + (y * r2)

Plugging in the given values, we have:

60,000 + (y * 2,000) = 54,000 + (y * 3,000)

Simplifying the equation, we get:

(y * 2,000) - (y * 3,000) = 54,000 - 60,000

Combining like terms, we have:

y * (-1,000) = -6,000

Dividing both sides of the equation by -1,000, we get:

y = 6

Therefore, Anissa's salary will be the same at both companies after 6 years. The salary at that point will be $60,000.