The second contractor is less expensive. See solution for the explanation.
Practice makes perfect
Mr. Thomas is planning to remove an old patio and install a new rectangular concrete patio that is 20 feet long, 12 feet wide, and 4 inches thick.
One constructor bid $2225 for the project. A second contractor bid $500 per cubic yard for the new patio and $700 for removal of the old patio. Let's find the cost of the total offer from the second constructor. First, let's find the volume of the patio. To do this let's find the dimensions in yards.
Dimension
Size
Rule
In Yards
Length
20 ft
1 ft≈ 0.333 yd
20* 0.333≈ 6.66
Width
12 ft
1 ft≈ 0.333 yd
12* 0.333≈ 4
Height
4 inches
1 inch≈ 0.02778 yd
4* 0.02778≈ 0.11
This tells us that the dimensions are about 6.66 by 4 by 0.11 yards. Since the volume of a rectangular prism is equal to the product of its dimensions, the volume of the patio is V=6.66* 4* 0.11≈ 2.93 cubic yards. Now, let's find the cost of the second constructor.
Cost = Removal + Volume* Cost per1 yd^3 ⇓
Cost = 700 + 2.93* 500 = 2165
Therefore, the second contractor bid $2165 for the project. Since the first contractor bid $2225, the second contractor is less expensive.
