MGF2106 Project 5: Linear Modeling and Geometry
In this project, you will be analyzing the predicted price increase in 3 different homes and calculating the cost of remodeling a house.
You will see 3 different lines which correspond to the value of a certain home after a renovation starting in the year 2023. The cost (y) is given in thousands of dollars and increasing each year (x). Note that each color of the line represents the color of the house you are interested in owning.
The red line is given by the equation: y = 30x + 300.
The blue line is given by the equation: y = 15x +375.
The green line is given by the equation: y = 10x + 400.
A picture containing line, plot, parallel, diagram Description automatically generated
Use the graph above to answer the following questions.
1. In what year will all the houses be worth the same amount? What is that amount?
2. Read the graphs to estimate the value for each home according to the year and fill in the table below.
2023
2025
2028
2033
Red
Blue
Green
3. In the year 2031, estimate from the graph how much more will the red house be worth than the green house. Write your answer below.
Use the equations below to answer the following questions.
The red line is given by the equation: y = 30x + 300.
The blue line is given by the equation: y = 15x +375.
The green line is given by the equation: y = 10x + 400.
4. Use the equations above to fill in the table below. Find the exact value of each house.
In 2.5 years
In 5 years
In 10 years
In 25 years
Red
Blue
Green
5. Use the equations above to fill in the table below. Find the exact time in years when the house will reach the given value, round to 1 decimal.
$420,000
$450,000
$750,000
$1,000,000
Red
Blue
Green
The house you bought needs to be remodeled with new flooring and new paint for the living room, kitchen, hallway, and three bedrooms.
All 6 of these areas are rectangular and here are the measurements for the flooring of each room:
· Living room is 15 ft x 20 ft
· Kitchen is 14 ft x 16 ft
· Hallway is 4 ft x 25 ft
· Bedroom 1 is 11 ft x 12 ft
· Bedroom 2 is 12 ft x 14 ft
· Bedroom 3 is 14 ft x 20 ft
6. Find the area of each room by filling in the table below.
Room
Area in Square Feet
Living Room
Kitchen
Hallway
Bedroom 1
Bedroom 2
Bedroom 3
7. Add up all the areas from above to decide how much material you need to cover your floor. What is the total area?
8. You are deciding between tile, carpet, or laminate for your flooring. In the table below, the cost of each is given per square foot. Calculate the total it would cost to cover all the square feet for those rooms by filling in the table below.
Flooring Type
Flooring Cost per square foot
Total Flooring Cost
Tile
$1.99
Carpet
$0.81
Laminate
$2.29
9. How much would you save installing carpet instead of laminate? Would you do that in your house? Why or why not?
All the walls are rectangular and here are the measurements of the walls for the paint needed:
· Living room has 2 walls both 12 ft x 18 ft with 2 total windows each 2 ft x 3 ft
· Kitchen has 1 wall 10 ft x 12 ft with one window 2 ft by 2.5 ft
· Hallway has 2 walls 12 ft x 25 ft
· Bedroom 1 has 3 walls 12 ft x 11 ft with 2 total windows each 2 ft by 2 ft
· Bedroom 2 has 3 walls 12 ft x 14 ft with 2 total windows each 2 ft by 3 ft
· Bedroom 3 has 3 walls 12 ft x 20 ft with 3 total windows each 2 ft by 3 ft
10. Calculate the area of wall space, the area of window space for each room (where needed), and then subtract the two to decide how much area must be painted for each room.
Room
Total Area of Walls
Total Area of Windows
Subtract Walls – Windows
Living Room
Kitchen
Hallway
Bedroom 1
Bedroom 2
Bedroom 3
11. What is the total area that needs to be painted in square feet?
12. If each gallon of paint covers 400 square feet, how many gallons of paint are required (keep in mind that you cannot buy part of a gallon of paint)?
13. If each gallon of paint costs $62, how much would it cost you for the paint needed for all the walls?
14. What other items would you need to purchase to paint the walls? Would you do this yourself or hire someone to complete the job?
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