Question

Marcus is working at a local pizzeria where he makes $12.50 per hour and is also working at the university bookstore where he makes $9.50 per hour. He must make at least $300 per week to cover his expenses but cannot work more than 30 hours per week in order to attend classes. Write a system of inequalities that models this situation where p represents the hours he works at the pizzeria and b represents the hours he works at the bookstore.

Answer 1

p+b
`\leq`30 .......(i)

12.50p+9.50b
`\geq`300 .......(ii)

Explanation:

Marcus Hourly Rate at the local pizzeria = $12.50 per hour

Marcus Hourly Rate at the university bookstore = $9.50 per hour

Let the number of hours worked at the local pizzeria=p

Let the number of hours worked at the university bookstore=b

Since he cannot work more than 30 hours per week in order to attend classes, the total of the hours:

p+b
`\leq`30 .......(i)

If he earns $12.50 for p hours at the local pizzeria,

Income from local pizzeria=12.50p

If he earns $9.50 for b hours at the university bookstore,

Income from university bookstore=9.50b

He must make at least $300 per week, therefore his total income must not be less than $300

Total Income=Income from Pizzeria + Income from University bookstore

12.50p+9.50b
`\geq`300 .......(ii)

Therefore the system of inequalities that models this situation is given as:

p+b
`\leq`30 .......(i)

12.50p+9.50b
`\geq`300 .......(ii)