# Investigation: Huey, Duey, and Luey

**Investigation: Huey, Duey, and Luey**

Huey, Duey, and Luey started working at different jobs on the first day of the year. They are hoping to save enough money to take a trip this summer. They’re excited because they know they earn the same amount of money each week so they can plan for their summer trip.

- Huey made the following table.

**Huey’s Total Earnings**

Weeks at new job / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9

Total $ earned / 220 / 440 / 660

- Complete the table knowing that Huey makes the same amount each week.
- How much is Huey making each week?

- Duey says he had earned $375 after the 3rd week and $750 after the 6th week.
- How much is Duey earning each week?
- Create a table like Huey’s to show how much Duey earns.

- Luey didn’t keep good records yet he did find some scribbles on the back of a magazine which stated something to the effect that “I have earned $425 so far at this job which seems a lot since I had only earned $170 three weeks ago.” How much does Luey earn every week?

- On the grid provided, graph linear models to show the earnings for each of the three brothers. Be sure to label each graph.

- Which line is the steepest? What does that mean in context of the brothers and their jobs?

- If Luey’s rate of earnings is doubled, what will happen to the graph of his earnings line? Will it be steeper than his brothers? Explain your reasoning.

- We use the word “slope” to describe “rate of change.” Why do you think we use the word “slope”?

Fred and Wilma want to remodel their house. They will need someone to install carpets, tile, and other types of flooring. Here are three different pricing options they’ve found.

- Which graph appears to be the steepest?

- Estimate how much Flora’s would charge to install 400 square feet of flooring. How much would Flora’s charge for 200 square feet of flooring? What is the unit rate for flooring installation at Flora’s?

- Estimate how much Freeda’s would charge to install 600 square feet of flooring. What is the unit rate for flooring installation at Freeda’s?

- Estimate how much Frank’s would charge to install 500 square feet of flooring. What is the unit rate for flooring installation at Frank’s?

- Fred and Wilma want to keep their costs to a minimum. Explain which company of the three options shown would work best for them to keep their flooring installation costs to a minimum.

- Fred and Wilma finally decided on their carpet. They spent $500 on all the carpet supplies. On the grid provided, graph three linear models to show total costs if Flora’s, Freeda’s, or Frank’s were used.

- Write the equations for each of the linear models:
- Flora’s total cost:
- Freeda’s total cost:
- Franks’s total cost: