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# Ronald's need to earn at least php 2,500 from his to job to cover his weekly expenses this week he can work for at most 42 hours is job as a gas station attendant pays php 52.50 per hour while his job as parking attendants pays php 40 per hour write a system of linear inequalities to the model the given situation? given this condition can ronald be able to meet his target of earnings php 2,500 why or why not justify your answers?

• Réponse publiée par: elaineeee

System of linear inequalities:

x + y ≤  4252.50x + 40y ≥ 2,500

Where:

x ≥ 65.6 hours  (at least or minimum of 65.6 hours)

y ≤ -23.6 (the most or maximum of -23.6 hours, non-existent hours)

Conclusion:

If Ronald has to work a maximum of 42 hours to earn at least 2,500 pesos, he will not be able to meet his target earnings because he has to work at least 65.6 hours as gas station attendant (when x ≥ 65.6 hours) and will not be able to work as parking attendant because y ≤ - 23.6 hours.

Step-by-step explanation:

System of linear equations:

A system where more than one equation involving at least two variables are involved. The system may have one solution, no solution, or many solution.

Inequality symbols and keywords:

At least or at minimum   ≥

At most or at maximum   ≤

Greater than   >

Less than   <

Ronald's jobs:

Gas station attendant: x

Parking attendant:  y

Total hours at most or at maximum: 42

Inequality:

x + y ≤  42

Work pay per hour:

As gas station attendant:  52.50x

As parking attendant: 40y

Target earnings at least or at minimum: 2,500

Inequality:

52.50x + 40y ≥ 2,500

Find the number of hours required for each job, x and y.

Equation (1):

x + y ≤ 42

y ≤ 42 - x

Solve the system by substitution method.

Substitute 42-x to y.

Equation (2):

52.50x + 40y ≥ 2,500

52.50x + 40 (42-x) ≥ 2,500

Find x the number of hours required as gas station attendant:

52.50x + 1,680 - 40x ≥ 2,500

12.5x  ≥ 2,500 - 1,680

12.5x/12.5 ≥ 820/12.5

x ≥ 65.6  hours

Ronald has to work at least 65.6 hours as gas station parking attendant.

65.6 hours is greater than 42 hours.

Find the number of hours  required as parking attendant:

y ≤ 42 - (65.6)

y ≤ - 23. 6 hours

Ronald will not be able to work as parking attendant if he has to work for 65.6 hours as gas station attendant.

Checking for equation purposes only:

Working hours:

65.6 hours + (-23.6 hours) ≤ 42 hours

42 hours ≤ 42 hours  (True)

Earnings:

52.50(65.6) + 40(-23.6) ≥ 2,500

3,444 - 944  ≥ 2,500

Php2,500 ≥  Php2,500  (True)

• Réponse publiée par: jasminsexy
Ihope this helps you
• Réponse publiée par: princessgarcia23
Can you use number set if its your topic if not, then discard this
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Ronald's need to earn at least php 2,500 from his to job to cover his weekly expenses this week he c...