Name ______________________________________ Date __________________ Period ___________

What’s My Equation, Inequality or Scenario?

1. At Work-It-Out, a gym membership is $50 per month with no registration fee. At Get Fit, the registration fee is $100 and membership costs $30 per month. Which equation could be used to find the number of months, m, for which the total cost of both gyms is the same?

A 100 + 30m = 50m Why or why not? ______________________________

B 50m = 30 + 100m Why or why not? ______________________________

C 100 + 50m = 30m Why or why not? ______________________________

D 50m = 100 – 30m Why or why not? ______________________________

2. Which of the following real-world problems can be modeled with the inequality 384 + 2x ≤ 6x?

A Marta charges a flat fee of $384 plus $2 per linear foot to decorate tables for a quinceanera. Carla charges $6 per linear foot to do the same. For what number of linear feet, x, will the cost of both decorators be the same?

Variable: x = _____________________ Equation or Inequality? Symbol: _______

B Shawna has made 384 campaign buttons for the student council election. She plans to make 2 more buttons each hour. Marguerite plans to make 6 campaign buttons per hour. For what number of hours, x, will Shawna have the same amount of campaign buttons as Marguerite?

Variable: x = _____________________ Equation or Inequality? Symbol: _______

C Super Clean house cleaning company charges $384 to power wash a house plus $2 per linear foot. Power Bright charges $6 per linear foot and no flat fee. For what number of linear feet, x, will the cost of Super Clean be more expensive than Power Bright?

Variable: x = _____________________ Equation or Inequality? Symbol: _______

D Mega Gym charges a $384 registration fee and $2 each time the gym is used. Super Gym charges a fee of $6 every time the gym is used. What number of times, x, will Super Gym need to be used to exceed the cost of Mega Gym?

Variable: x = _____________________ Equation or Inequality? Symbol: _______

3. Jose and Maris work for different car dealerships. Jose earns a monthly salary of $3,500 plus a 6% commission on his sales, x. Maris earns a monthly salary of $4,000 plus a 4% commission on her sales, x. For what value of sales, x, will Jose’s earnings be greater than Maris’ earnings?

Choose the inequality that could be used to solve this problem.

A 3,500 + 6x > 4,000 + 4x Why or why not? ______________________________

B 3,500 + 0.06x > 4,000 + 0.04x Why or why not? ______________________________

C 3,500 + 0.6x > 4,000 + 0.4x Why or why not? ______________________________

D 3,500 + 0.06x < 4,000 + 0.04x Why or why not? ______________________________

4. Which of the following scenarios can be modeled with the equation 365 +125x = 175 + 250x?

A Rent-a-Tent rents party tents for a flat fee of $365 plus a daily fee of $125. Superior Rentals rents party tents for $175 per day plus a flat fee of $250. For what number of days, x, will the cost of Rent-a-Tent be equal to the cost of Superior Rentals?

Variable: x = _____________________ Equation or Inequality? Symbol: _______

B Rent-a-Tent rents party tents for a flat fee of $365 plus a daily fee of $125. Superior Rentals rents party tents for $250 per day plus a flat fee of $175. For what number of days, x, will the cost of Rent-a-Tent be equal to the cost of Superior Rentals?

Variable: x = _____________________ Equation or Inequality? Symbol: _______

C Rent-a-Tent rents party tents for a flat fee of $365 plus a daily fee of $125. Superior Rentals rents party tents for $250 per day plus a flat fee of $175. For what number of days, x, will the cost of Rent-a-Tent exceed the cost of Superior Rentals?

Variable: x = _____________________ Equation or Inequality? Symbol: _______

D Rent-a-Tent rents party tents for a flat fee of $125 plus a daily fee of $365. Superior Rentals rents party tents for $175 per day plus a flat fee of $250. For what number of days, x, will the cost of Rent-a-Tent be equal to the cost of Superior Rentals?

Variable: x = _____________________ Equation or Inequality? Symbol: _______

5. A handyman charges a flat rate of $150, plus $25 per hour for house painting. A painter charges $55 per hour for house painting. Which equation could be used to determine, h, the number of hours each would have to work for their fees to be the same?

A 150 – 25h = 55h Why or why not? ______________________________

B 150 + 25h = 55h Why or why not? ______________________________

C 150 – 55h = 25h Why or why not? ______________________________

D 55h + 150 = 25h Why or why not? ______________________________

6. Purple Taxi has no pick-up fee, but charges $0.25 per mile. ABC Taxi charges $3 for pick-up and $0.15 per mile. Which inequality can be used to find the number of miles, n, for which the cost of a cab ride with Purple Taxi exceeds the cost of a cab ride with ABC Taxi?

A 0.25n ≥ 3 + 0.15n Why or why not? ______________________________

B 0.25n + 3 < 0.15n Why or why not? ______________________________

C 0.25n > 0.15n + 3 Why or why not? ______________________________

D 3 + 0.15n > 0.25n Why or why not? ______________________________

Practice1. Derrick’s Doggie Day Care charges a $12 registration fee plus $5 per hour for pet sitting. Pauline’s Pooch Park charges $3 per hour plus an $18 registration fee. Which inequality below can be used to find the number of hours, h, for which the cost of Derrick’s Doggie Day Care is at most the cost of Pauline’s Pooch Park?

A 12 + 5h ≥ 3h + 18 Why or why not? ______________________________

B 5h + 12 > 18 + 3h Why or why not? ______________________________

C 12 + 5h < 3h + 18 Why or why not? ______________________________

D 12 + 5h ≤ 18 + 3h Why or why not? ______________________________

2. Billie needs to have her refrigerator repaired. She contacts two appliance companies and is given the rates shown in the table.

Company Service Call Charge

Charge Per Hour

Acme Repair $49 22.50Ace Repair $0 34.75

Write an inequality that can be used to find the number of hours, n, for which Ace’s total charge is less than or the same as Acme’s total charge?

3. In any triangle, the length of the longest side must be less than the sum of the lengths of the other two sides. Write an inequality that can be used to find the value of x for the triangle shown below.

4. D. J. plans to earn money for an electric guitar. He has two options:

Option 1: His grandmother will pay him $250 to paint her tool shed, and he can work for his dad for $10 per hour. He will save 80% of the money he earns.

Option 2: He can work for his uncle for $16 per hour. He will save 75% of the money he earns.

Which equation below can be used to find the number of hours, h, that D. J. will need to work in order for the money he saves from each option to be the same?

A Why or why not? ______________________________

B Why or why not? ______________________________

C Why or why not? ______________________________

D Why or why not? ______________________________

Write your own real-world problem for each of the following.

5. 21 + 1.5n = 28 – 2n 6. 1.5x ≥ 0.5x + 3