A homeowner wanted to improve the value of his home by putting tile flooring in three of his rooms. He researched the different types of tile and decided on two types: ceramic tile and decorative tile.
He found that he could purchase the ceramic tile for $5.35 per square foot installed and the decorative tile would be $8.20 per square foot installed.
Use this information to answer the following questions. Use equation Editor to write mathematical expressions and equations. First save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting.
1. Write an expression that would represent the cost of ceramic tile (use “c” to represent the ceramic tile)
2. Write an expression that would represent the cost of the decorative tile (use “d” to represent the decorative tile)
3. The homeowner is planning to spend no more than $3,600 for the flooring. Write an inequality that demonstrates how much money he is willing to spend for the two types of tile.
4. He decides to tile Room 1 and Room 2 with ceramic tile only. The dimensions of Room 1 are 20 feet by 20 feet and the dimensions of Room 2 are 15 feet by 19 feet. Write an expression that would represent the total cost of the two rooms and find the solution.
5. There is one more room he would like to tile with just decorative tile. Given how much he has spent on the previous two rooms; write an inequality that represents the maximum amount of money he has to spend on the decorative tile.
6. The dimensions of Room 3 are 18 feet by 9.5 feet. Find the total area of the room and determine, using the inequality from #5, if he has enough money to tile Room 3 with the decorative tile. If he does, how much additional money does he have left? If he doesn’t, how much extra money does he need?
Part B
The landscaper that maintains Mrs. Jones’ lawn charges a flat fee of $30.00 for each job plus $12.40 per hour for labor.
a. Translate the problem situation into an algebraic equation using C for total cost and h for hours.
Starting next week, the landscaper is raising his hourly rate to $15.00 per hour but reducing his flat fee to $27.45.
b. Translate the new problem situation into an algebraic equation using c for total cost and h for hours.
c. Mrs. Jones has decided to have the landscaper come for 5 hours per week. How much more money will she be paying each week at these new rates? Use the equations you wrote in parts a and b to find your answer making sure to show all the work.
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1. The expression that represents the cost of ceramic tile (c) is: c = 5.35
2. The expression that represents the cost of decorative tile (d) is: d = 8.20
3. To demonstrate how much money the homeowner is willing to spend for the two types of tile, we can add the cost of ceramic tile and decorative tile and set it less than or equal to $3,600. The inequality would be: c + d ≤ 3600
4. To calculate the total cost of tiling Room 1 and Room 2 with ceramic tile only, we need to find the area of each room and multiply it by the cost per square foot of ceramic tile installed.
The area of Room 1 is 20 ft * 20 ft = 400 sq ft
The area of Room 2 is 15 ft * 19 ft = 285 sq ft
The expression for the total cost of the two rooms is: Total Cost = (c * Area of Room 1) + (c * Area of Room 2)
Substituting the values:
Total Cost = (5.35 * 400) + (5.35 * 285)
Total Cost = $2140 + $1524.75 = $3664.75
So, the total cost of tiling Room 1 and Room 2 with ceramic tile is $3664.75.
5. To represent the maximum amount of money the homeowner can spend on decorative tile, we need to subtract the cost of tiling Room 1 and Room 2 from the total budget of $3,600. The inequality would be:
Maximum Budget for Decorative Tile = 3600 - Total Cost of Room 1 and Room 2
Substituting the value of the total cost of Room 1 and Room 2 from question 4:
Maximum Budget for Decorative Tile = 3600 - 3664.75
6. To find the total area of Room 3, we multiply the length and width of the room:
Area of Room 3 = 18 ft * 9.5 ft = 171 sq ft
Using the inequality from question 5, we can check if the homeowner has enough money to tile Room 3 with decorative tile. If the Maximum Budget for Decorative Tile calculated in 5 is greater than or equal to the cost of decorative tile per square foot installed (d), then the homeowner has enough money.
If the homeowner has enough money to tile Room 3, we can subtract the cost of tiling Room 3 from the maximum budget to find the additional money left:
Additional Money Left = Maximum Budget for Decorative Tile - (d * Area of Room 3)
If the homeowner doesn't have enough money to tile Room 3, we can find the extra money needed:
Extra Money Needed = (d * Area of Room 3) - Maximum Budget for Decorative Tile
Substitute the values to find the result.
Part B:
a. The algebraic equation that represents the total cost (C) with the flat fee (F) and hours of labor (h) can be written as C = F + (12.40 * h).
b. The new algebraic equation that represents the total cost (c) with the new flat fee (f) and hours of labor (h) can be written as c = f + (15.00 * h).
c. To find out how much more money Mrs. Jones will be paying each week at the new rates, subtract the new total cost from the old total cost: Difference in Cost = c - C. Substitute the values and calculate the difference.