Question

7. Alex makes $30,000 a year at his job

and gets $2,500 a year raise every year.
Sydney makes $40,000 a year and gets a
$2,000 raise every year. How many years
will it take for them to make the same
salary?

Answer 1

It will take them 20 years to make the same salary

Explanation:

Let us solve the question

Assume that they will have the same salary after x years

∵ Alex makes $30,000 a year at his job

∵ He gets a $2,500 a year raise every year

∵ He will work x years

→ That means his salary is the sum of a fixed amount and the raise times x

∴ His salary = 30000 + 2500(x) ⇒ (1)

∵ Sydney makes $40,000 a year

∵ He gets a $2,000 raise every year

∵ He will work x years

→ That means his salary is the sum of a fixed amount and the raise times x

∴ His salary = 40000 + 2000(x) ⇒ (2)

∵ They will make the same salary after x years

→ Equate (1) and (2)

∴ 30000 + 2500x = 40000 + 2000 x

→ Subtract 30000 from both sides

∴ 2500x = 2000x + 10000

→ Subtract 2000x from both sides

∴ 500x = 10000

→ Divide both sides by 500

∴ x = 20

∴ It will take them 20 years to make the same salary