Susan earns $91 per day. She gets paid $14 for each hour of overtime she works, but she cannot earn more than $147 in a day. Write an inequality that represents the relationship between the number of hours of overtime Susan worked, x, and her earnings. Calculate the amount of overtime Susan can work.

The amount of overtime Susan can work is 4 hours.

Step-by-step explanation:

It is given that, Susan earns $91 per day.

This means that, her usual pay is $91 which is the Susan's default pay per day.

From the given information,

It is known that, she cannot earn more than $147 in a day. The amount of money she could get for each additional hour = $14

The question is asked to write an inequality,

Let the number of overtime Susan worked be 'x'.

The relationship between the number of hours of overtime Susan worked and her earnings is given by:

(amount of money for each additional hour * number of overtime hours worked) ≤ (maximum pay Susan can earn - Susan's default pay)

⇒ 14x ≤ (147-91)

⇒ 14x ≤ 56

Therefore, the above relation 14x ≤ 56 gives the amount of overtime Susan can work.

Put x = 1 hour overtime,

14 ≤ 56

Put x = 2 hours overtime,

28 ≤ 56

Put x = 3 hours overtime,

42 ≤ 56

Put x = 4 hours overtime,

56 ≤ 56

Therefore, Susan can work up to 4 hours of over time.