Answer:
The possible values of the number of hours clearing tables are 2 , 3 , 4 , 5 hours
Explanation:
* Lets explain how to solve the problem
- Madelyn is making $20 per hour life guarding
- She is making $12 per hour clearing tables
- She can work no more than 13 total hours
∴ The greatest time she can work is 13 hours (≤)
- She must earn no less than $180
∴ The least money she wants to earn is $180 (≥)
- If Madelyn worked 8 hours life guarding and assume that she
worked x hours clearing tables
∵ She can work no more than 13 hours
∴ 8 + x ≤ 13
- Subtract 8 from both sides
∴ x ≤ 5 ⇒ (1)
∵ She must earn no less than $180
∴ 8 × 20 + x × 12 ≥ 180
∴ 160 + 12x ≥ 180
- Subtract 60 from both sides
∴ 12x ≥ 20 ⇒ (2)
- From equation (1) ⇒ x = 1 , 2 , 3 , 4 , 5
- Substitute x in equation (2) by these values to find the right values
of x
# If x = 1
∴ 12(1) ≥ 20
- But 12 is less than 20
∴ x can not be 1
# x = 2
∴ 12(2) ≥ 20
∴ 24 ≥ 20
- 24 is greater than 20 then x can be 2
∵ 3 , 4 , 5 greater than 2
∴ All of them give answers greater than 20
∴ x can be 3 , 4, 5
∵ x represents the number of hours for clearing tables
∴ The possible values of the number of hours clearing tables are
2 , 3 , 4 , 5 hours