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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