I need to know if I did this right. Below is story problem. It has questions labeled a-f. Under each lettered question, I provided an answer, but I am not confident with my outcome. Can you read it over and tell me if I did it right? If not can you steer me in the right direction.
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 $5.00 per square foot installed and the decorative tile would be $6.00 per square foot installed.
Use this information to answer the following questions.
Write an expression that would represent the cost of ceramic tile (use c to represent the ceramic tile)
c=$5.00b
Write an expression that would represent the cost of the decorative tile (use d to represent the decorative tile)
D=$6.00b
The homeowner is planning to spend no more than $6,000 for the flooring. Write an inequality that demonstrates how much money he is willing to spend for the two types of tile.
C<, or equal to $6,000
He decides to tile Room 1 and Room 2 with ceramic tile only. The dimensions of Room 1 are 30 feet by 30 feet and the dimensions of Room 2 are 10 feet by 12 feet. Write an expression that would represent the total cost of the two rooms and find the solution.
Room 1: First I calculate total square feet by figuring out the area¡ A=s^2¡30*30=900 square feet
Now I figure out cost by calculating the cost of square footage:
Cost=price per square foot multiplied by the number of square feet.
$5.00*900 square feet =$4,500
Solution for room 1 is $4,500
Room 2: Again, I need to calculate total square feet by finding the
Area...a=s(2): 10*12=120
Now, I figure out cost by calculating the cost of square footage:
Cost=price per square foot multiplied by the number of square feet.
$5.00*120=600
Solution for room 2 is $600
Now, to find the total cost of the two rooms; I would add the total cost of room1 ($4,500) and the total cost of room 2($600) together:
$4,500+$600=$5,100
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.
The owner wants to spend no more than $6,000 on flooring; he has already spent $5,100. We subtract 5,100 from 6,000 to see how much money he has left to spend on the flooring, or the maximum he has left: $6,000-$5,100=900
An inequality that would represent the maximum amount would be: c<, or equal to 900
The dimensions of Room 3 are 8 feet by 12 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.
I need to calculate total square feet by finding the
Area...a=s(2):8*12=96 square feet
Now I figure out cost by calculating the cost of square footage:
Cost=price per square foot multiplied by the number of square feet.
$6.00*96=$576
576<900
Therefore, the homeowner has enough money to use the decorative tile for room
three.
Let's go through each question and answer to check if you did it correctly:
a) Write an expression that would represent the cost of ceramic tile.
You answered: c = $5.00b
This is correct. The expression c = $5.00b represents the cost of ceramic tile per square foot.
b) Write an expression that would represent the cost of the decorative tile.
You answered: D = $6.00b
This is incorrect. It should be d = $6.00b, not D. The correct expression is d = $6.00b.
c) The homeowner is planning to spend no more than $6,000 for the flooring. Write an inequality that demonstrates how much money he is willing to spend for the two types of tile.
You answered: C ≤ $6,000
This is incorrect. It should be c + d ≤ $6,000, as you need to consider the cost of both types of tile. So the correct inequality is c + d ≤ $6,000.
d) Write an expression that would represent the total cost of Room 1 and Room 2.
You answered: $4,500 + $600 = $5,100
This is incorrect. The correct expression is c * Room 1's area + c * Room 2's area. The area of Room 1 is 900 square feet, and the area of Room 2 is 120 square feet. So the correct expression is $5.00 * 900 + $5.00 * 120 = $4,500 + $600 = $5,100. Your answer is correct.
e) Write an inequality that represents the maximum amount of money he has left to spend on the decorative tile.
You answered: c ≤ 900
This is incorrect. The correct inequality is d ≤ 900 since we're referring to the maximum amount of money he has left to spend on the decorative tile. So the correct inequality is d ≤ 900.
f) Find the total area of Room 3 and determine, using the inequality from #e, if he has enough money to tile Room 3 with the decorative tile.
You answered: The homeowner has enough money to use the decorative tile for Room 3.
This is correct. You calculated the area of Room 3 correctly as 96 square feet. Then you calculated the cost of tiling Room 3 with decorative tile correctly as $6.00 * 96 = $576. Since $576 is less than or equal to $900 (the maximum amount he has left to spend on decorative tile), he has enough money to tile Room 3 with decorative tile.
Overall, you did well. Only two answers needed correction, and you correctly solved the math problems to find the total cost and determine if the homeowner has enough money.