Multi-Step Inequalities Word Problems

A personal trainer charges a one-time fee of $60 plus $25 for each individual session. A fitness club charges a yearly fee of $450 plus $10 for each session with a personal trainer. At what point does it become cheaper to join the gym as opposed to working with only a personal trainer?

Remember there are two sides to every inequality.

• After 26 visits with a trainer.

• After 15 visits with a trainer.

• On the 26th visit.

• It is never cheaper.

The sophomore class is planning a picnic. The cost of a permit to use a city park is $250. To pay for the permit, there is a fee of $0.75 for each sophomore and $1.25 for each guest who is not a sophomore. Two hundred sophomores plan to attend. How many guests must attend for the sophomores to pay for the permit?

• The sophomores need no more than 80 guests.

• The sophomores need more than 320 guests.

• The sophomores need less than 320 guests.

• The sophomores need at least 80 guests.

The student council is sponsoring a concert as a fund raiser. Tickets are $3 for students and $5 for adults. The student council wants to raise at least $1,000. If 200 students attend, how many adults must attend?

• between 80 and 320 adults

• 80 adults

• 320 adults

• At least 80 adults

A small airplane must carry less than 3,050 pounds of passengers, luggage and mail. The mail for the day weighs 490 pounds. If there are 10 passengers and the average passenger weighs 185 pounds, how many pounds of luggage can each passenger bring aboard?

• more than 71 lbs of luggage.

• between 71 and 238 lbs of luggage.

• less than 238 lbs of luggage

• less than 71 of luggage.

• x > 2
• x > 5
• x >15
• x > 50

Solve. 3(k-5) + 9k ≥ -3

• k ≥ 0

• k ≤ -1

• k≥ 1

• k≥ 2

For what values of x is the perimeter of the figure greater than 112 ​meters?

• A
• B
• C
• D

22 < 6c + 4

• 11>c

• 3>c

• 11<c

• 3<c

-2x + 3(-4x + 6) ≤116

• x ≤ -7

• x ≥ 29

• x ≥ -7

• x ≤ 29