Solving Multistep Inequalities: Budgeting and Limits

A store sells pencils for $0.50 each and erasers for $0.75 each. If you want to spend no more than $10, how many pencils (p) and erasers (e) can you buy? Write the inequality and interpret the solution set.

• The inequality is 3p + 2e ≤ 30, indicating a different budget limit.

• The inequality is 4p + e ≤ 15, which does not reflect the correct pricing.

• The inequality is p + e ≤ 20, representing the total number of items you can buy.

• The inequality is 2p + 3e ≤ 40, representing the combinations of pencils and erasers that can be purchased without exceeding $10.

A school is planning a field trip and has a budget of $300. The cost per student is $15, and there are 20 students. Write an inequality to represent the maximum number of students (s) that can attend the trip and interpret the solution set.

• s < 20

• s ≥ 20

• s ≤ 20

• s > 20

A gardener has 50 feet of fencing to create a rectangular garden. If the length (l) is twice the width (w), write an inequality to represent the possible dimensions of the garden and interpret the solution set.

• 0 < w < 20 and l = 2w < 40

• 0 < w < 15 and l = 2w < 30

• 0 < w < 30 and l = 2w < 60

• 0 < w < 25/3 and l = 2w < 50/3

A concert hall has a seating capacity of 500. If tickets are sold for $20 each and the total revenue must be at least $8000, write an inequality for the number of tickets (t) that can be sold and interpret the solution set.

• t < 400

• t > 500

• t = 300

• 400 <= t <= 500

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If you want to spend no more than $100, write an inequality for the number of miles (m) you can drive and interpret the solution set.

• m ≤ 300

• m ≤ 400

• m ≤ 250

• m ≤ 350

A gym has a maximum capacity of 150 members. If currently there are m members and 20 new members want to join, write an inequality to represent the situation and interpret the solution set.

• m + 20 < 150

• m + 20 = 150

• m + 20 ≤ 150

• m + 20 ≥ 150

A baker can make a maximum of 200 cookies in a day. If each cookie requires 0.5 cups of flour and 0.25 cups of sugar, write an inequality for the total amount of flour (f) and sugar (s) used and interpret the solution set.

• f + s = 200

• f + s ≤ 150

• f + s ≤ 100

• f + s ≥ 150

A student has a budget of $50 to spend on books. If each book costs $12 and the student wants to buy at least 3 books, write an inequality for the number of books (b) the student can buy and interpret the solution set.

• 3 <= b <= 4

• b > 4

• b < 3

• b = 5

A factory produces toys and has a limit of 1000 toys per day. If each toy requires 2 hours of labor and the factory has 1600 hours available, write an inequality for the number of toys (t) that can be produced and interpret the solution set.

• t ≤ 600

• t ≤ 1000

• t ≤ 400

• t ≤ 800