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3.03 Applications of Inequalities

Solve each problem. Be sure to include the following:

• Define all variables.

• Write and solve each inequality.

• Show ALL solution steps.

• Write the solution set in set-builder notation.

1. A number is less than one-fourth the sum of eight times the number and four.

     

2. Negative three times a number plus four is no more than the number minus eight.

     

3. Two-thirds of a number added to six is at least twenty-two.

     

4. A realtor is paid a base salary of $20,000 a year plus 10% commission on all property sales. What are the sales needed to ensure an annual income greater than $50,000?

     

5. A car salesperson is paid a base salary of $30,000 a year plus 9% commission on all sales. What are the sales needed to ensure an annual income greater than $75,000?

     

6. A high school technology club needs to raise money for a mobile computer lab. They plan to hold a community picnic. Tickets cost $10 each. A local business donated $6500, but the club needs at least $10,000. How many tickets will the club need to sell?

     

7. A high school band needs to raise money for a new bandstand. They plan to have a dance after their next football game. Tickets cost $4 each. A local business donated $1,500, but the band needs at least $3,500. How many tickets will the club need to sell?

     

8. Ten is no more than four times the sum of twice a number and three.

     

9. Rachel earns $150 per month from her job at the local library plus $6.00 per hour from babysitting jobs. If she wants to earn at least $300 this month, how many hours will she need to babysit?

     

10. Michael earns $200 per month from his job at the local bowling alley and $5.00 per hour delivering newspapers. If he wants to earn at least $500 this month, how many hours will he need to deliver newspapers?

     

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