Construction Math Part 1 PDF

An 18\' long, 2\" x 4\" fir stud wall has double top plates, a single bottom plate and fourteen 8\' studs. Fir costs \$520 per thousand board feet. How much does the lumber for this wall cost? Do not allow for waste. **\$59** [Construction Math -] [To calculate the cost of lumber for the wall:]...

An 18\' long, 2\" x 4\" fir stud wall has double top plates, a single bottom plate and fourteen 8\' studs. Fir costs \$520 per thousand board feet. How much does the lumber for this wall cost? Do not allow for waste. **\$59** [Construction Math -] [To calculate the cost of lumber for the wall:] 1. **Formula for board feet**[:] - [Board feet = Number of pieces × Thickness (in inches) × Width (in inches) × Length (in feet) ÷ 12] 2. **Convert plates to match studs**[:] - [Plates (double top + single bottom) are 18\' long: 18 × 3 = 54 feet of 2x4.] - [Convert 54 feet into 8\' sections to match studs: 54 ÷ 8 = 6.75 (round up to 7 pieces).] 3. **Total pieces of 2x4**[:] - [7 pieces for plates + 14 studs = 21 pieces total.] 4. **Calculate total board feet**[:] - [21 × 2 × 4 × 8 ÷ 12 = 112 board feet.] 5. **Calculate cost**[:] - [Price per board foot: \$520 ÷ 1000 = \$0.52.] - [Total cost: 112 × \$0.52 = \$58.24.] [The total cost of the lumber is ]**\$58.24**[.] 2. Calculate the linear footage for a 2x6 wall that is 8' tall and 10' long. Studs are 16" (OC). Add for the bottom plate and double top plate. Do not account for any waste. **102** [Construction Math -] [For this problem, we are calculating the total linear feet of boards needed to frame a 8\' x 10\' wall.] 6. **Plates (Double Top + Bottom)**[:] - [The wall is 10' long.] - [Each top plate and bottom plate are 10' long: 10' × 3 = 30' total.] 7. **Calculate studs**[:] - [Convert wall length to inches: 10' × 12 = 120".] - [Divide by 16" spacing: 120" ÷ 16" = 7.5 studs.] - [Round up to 8 studs (since 16" is the maximum spacing).] - [Add one more stud for the start of the wall: 8 + 1 = 9 studs total.] 8. **Stud linear footage**[:] - [Each stud is 8' tall: 9 × 8' = 72'.] 9. **Total linear footage**[:] - [30' for plates + 72' for studs = ]**102' total**[.] [The total linear footage of boards needed is ]**102 feet**[.] [Show Book Image Hint](https://contractorcourses.com/) 3. What is the maximum size building that can be built on a 100\' x 150\' lot with a 10 foot setback on each side and the rear, and a 15 foot setback on the front? **10,000 square feet** [Construction Math -] [A setback is a distance from the property line that cannot be built on. ] [If the property is 100 feet wide and has a 10 foot setback on each side, the width that can be built on is 80 feet.] [If the property is 150 feet deep and has a 10 foot setback on the rear and a 15 foot setback at the front, the depth that can be built on is 125 feet.] [80\' x 150\' = 10,000 square feet of buildable area] 4. A 5 gallon bucket of concrete sealer covers 250 sq. feet. How many buckets will it take to seal a concrete slab that is 200\' by 125\'? **100** [Construction Math -] [First, find the total area of the slab by multiplying the length by the width, then divide the total by 250 to determine how many 5 gallon buckets are required.] [200 x 125 = 25,000 sq. feet] [25,000 / 250 = ]**100 five gallon buckets** 5. A blueprint is drawn to a scale of 3/16\" = 1\'-0\". What will 4 1/2\" on the blueprint equate to for the real structure? **24\'** [Construction Math -] [A blueprint is drawn to a scale of 3/16\" = 1\'-0\". What will 4 1/2\" on this drawing equal?] **Method 1:** [Convert 3/16 to a decimal: 3 / 16 = 0.1875] [Divide the 4 1/2\" (4.5) by the 0.1875 to determine how many 3/16ths there are in 4.5 inches.] [4.5 /.1875 = ]**24** **Method 2:** [Convert 4 1/2\" to 4.5] [Multiply 4.5 by 16 to determine how many 16ths are in 4.5] [4.5 x 16 = 72] [Divide that number by the \"scale\" which in this case is 3 since 3/16 = 1\"] [72 / 3 = ]**24** 6. A building slab will be 25\' x 90\' x 8\". How many cubic yards of concrete will be needed? (Note: assume that the grade will be perfectly level and that there will be no crown or slope in the slab. Do not account for waste.) **56 yd.³** [Construction Math -] [25×90 = 2250 ft.²] [multiply by 8 inches (8 inches is.66 of a foot) =  2250 X.66 = 1485 ft.² , divide by 27] 7. A commercial piece of property has to be re-seeded. The property is 1,500\' x 1,800 \'. The lot contains a two story building that is 150\' x 150\' and a one story building that is 40\' x 40\'. Also, there is a 100\' x 200\' parking area and 2,000 sq ft of entrance road and walkways. What is the cost to re-seed the property if seed is \$27 per lb and covers 2,500 sq ft per lb? Add labor as 15% of the seed cost. **\$32,961** [Construction Math -] [1,500 x 1,800 = 2,700,000 total square feet of the lot.\ 150' x 150' = 22,500 SQ. feet of the two-story building\ 40' x 40' = 1,600 SQ. feet of the one story building\ 100' x 200' = 20,000 of feet of parking area\ 2,000 SQ. feet of entrance road and walkways is given] [2,700,000 Total Area] [- 22,500 Two story building] [- 1,600 One story building] [- 20,000 Parking area] [- 2,000 Entrance road and walkways] [2,653,900 Area to be seeded] [2,653,900 / 2,500 (amount of coverage per pound) = 1,061.56 lbs. of seed needed] [1,061.56 \$27 = \$28,662 for seed] [\$28,662 x 15% = \$4,299 for labor] [\$28,662 + \$4,299 = \$32,961] 8. A contractor bids a job for \$60,000, plus 10% for overhead and 8% profit. What will be the contractor\'s bid?\ \ (In this case the word \"profit\" should be viewed as \"markup\". Typically PSI will use the word profit even when the only possible answer is clearly just a mark up.) **\$71,280** [Construction Math -] [Take the \$60,000 and add the 10% overhead to calculate ALL costs. Then add the 8% profit.] [\$60,000 x 1.10 = \$66,000] [\$66,000 x 1.08 =]** \$71,280** 9. A contractor is looking to bid on a job to place and finish fiber mesh concrete. The fiber mesh concrete costs the contractor \$82 per cubic yard. Regular concrete is \$75 per cubic yard and requires steel mesh to be installed, which cost \$.10 per square foot. The contractor will use a subcontractor who charges \$3.75 per square foot to place and finish the fiber mesh concrete. What is the cost for the contractor to provide a 500 square foot slab that is 4 inches thick? Do not account for waste. **\$2,383** [Construction Math -] [The sentence about regular concrete and steel mesh is only in the question to confuse you. To solve, you need to find the labor cost (\$3.75 x 500 square feet = \$1,875) and add the material cost. The material cost is calculated by first converting \$82 per cubic yard to cubic feet. 82 / 27 = \$3.04 per cubic foot. Next find the cubic feet for the slab by multiplying 500 by 1/3 (the slab is 4\" thick or 1/3 of a foot) to get 167 cubic feet. 167 x \$3.04 = \$507.68. ] [\$1,875 (labor) + \$507.68 (materials) = \$2,382.68  ] [NOTE: When numbers come out to be long decimals (for example 3.03703704) it\'s best to round up (3.04)] [ ] 10. A cut stake is being set for the excavation of a trench using a building level (transit). The bottom of the trench will be at elevation 94.00 feet. A rod reading of 4.70 feet is taken on a benchmark whose elevation is 102.50 feet. The rod reading on the mark on the cut stake is 6.20 feet. What should the cut stake be marked **7.00** [Construction Math -] [Construction Math:] [Add the reading of 4.7 to the benchmark elevation of 102.5 for a total of 107.2. This compensates the difference of the benchmark elevation and your transit height. ] [Next, add the 6.2 reading to the elevation of 94 for a total of 100.20.] [Subtract the 100.2 from the 107.2 for a total of 7.  The cut stake would be marked to excavate 7 feet to reach the 94-foot elevation.   ] [ ] [For more information on stake markings and elevation watch this video - ] 11. A rectangular building with a gable roof will be 80\' x 36\'. The rafters will be spaced 32\" on center. How many total rafters will be needed? **62** [Construction Math -] [80 feet X 12inches = 960 total inches.] [960 divided by 32 inches o.c.= 30 rafters.] [You need 2 rafters on each side for the 36' span: 2 x 30 rafters = 60 Rafters.] [Since the calculation for the number of rafters is based on On Center, you\'ll need one more set of rafters for the end. 1 x 2 = 2 Rafters] [60 Rafters + 2 Rafters = 62 Rafters total] 12. A sidewalk 100\' long slopes at 1/16\" per foot. What is the total drop or rise at one end? **0.52\'** [Construction Math -] [Convert 1 / 16 to a decimal 1/16 =.0625\"] [Multiply slope per foot decimal by total length.0625 X 100 = 6.25\"] [This means the total slope is 6.25 inches] [To come up with the number of feet of the slope divide the number of inches by 12] [6.25\" divided by 12 = 0.52\'] 13. A subcontractor bids a unit cost of \$19.50 per square foot for labor and materials to provide and install ceramic tile. The cost for the subcontractor to do the tile work breaks down to 50% split for profit and material. There is 2500 sq. ft. of floor tile in the project. The owner wants to upgrade the tile. The material will increase \$2.25 per square foot. What is the amount of the change order to the original contract amount to upgrade the floor tile? The contract allows a 20% markup. **\$6,750** [Construction Math -] [The line in this question about the 50% split is irrelevant to finding the answer. ] [Multiply the increase per square foot by the square footage to get the total increase amount.\$2.25 (increase amount) X 2,500 (sq. ft) = \$5,625 ] [Add the 20% markup by multiplying \$5,625 by 1.2 = \$6750] 14. An underground tank with inside dimensions of 8\' 3/4\" x 4\' 1/2\" and 4\' deep will be filled with sand. The total cubic yards of sand required to fill the tank is\_\_\_\_\_\_\_\_\_\_\_. Make no allowance for compaction of sand. **Less than 5.00** [Construction Math -] [Multiply the length x the width x the depth to get the total cubic feet, then divide by 27 to get the cubic yards. You will need to convert the fractions to decimal feet.] [¾" calculation: 3 divided by 4 =.75 Then.75 / 12 =.0625 (3/4\" =.0625 feet)] [½" calculation: 1 divided by 2 =.5 Then.5 / 12 =.04] [Now we have what we need to solve the problem] [8.0625 x 4.04 x 4 = 130.29 cubic feet Then 130.29 / 27 = ]**4.82 cubic yards** 15. Calculate the number of cubic yards of asphalt to cover a dumpster pad with 6 inches of material, where the length of the pad is 20 feet and the width is 15 feet. **6 cubic yards** [Construction Math -] [(study guide) Multiply length x width to get the area (20x15 = 300 sq. ft.)] [Divide area by thickness in feet.] [To find the cubic ft. 300 x.5 (this represents the 6\" or half a foot) = 150 cubic feet] [Convert to cubic yards: 150 / 27 = 5.55 cubic yards] 16. Given: A 24\' long x 52\' wide, 8\" thick slab on grade is to be edge-formed with 2x8 pressure treated pine. How many board feet of pine will be required to construct a 2\" thick edge-form for the slab on grade described above? **203 board feet** [Construction Math -] [First you need to calculate the total length of 2x8 needed, and then convert it to board feet.] [24' + 24' +52' +52' = 152 lineal feet] [To convert the lineal feet to board feet, simply multiply the type of board used by the total lineal feet and divide by 12. This will give you the total board footage.] [(2 x 8 x 152) / 12 = 202.666 or ]**203 board feet** 17. Given: Concrete is \$125 per cubic yard. A concrete pump is a flat rate of \$625 for this job.  You need to pour an 8" x 16" concrete tie beam for a building that is 28' x 50'. Using only the above information, what will it cost to pour the tie beam? **\$1,375** [Construction Math -] [First, you need to find the total length of the tie beam, then convert the 8" x 16" measurements to feet. Now multiply the width x the height x the length of the tie beam to get the total cubic feet of concrete. Then divide this number by 27 to get the cubic yards. Be sure to add the concrete pump rental.] [28' + 28' + 50' +50' = 156 lineal feet of tie beam] [8" is divided by 12" to become.67] [16" is divided by 12" to become 1.33] [.67 x 1.33 x 156 = 139 cubic feet of concrete] [139 cubic ft. divided by 27 = 5.14 cubic yards of concrete] [5.14 has to be rounded up to 6 cubic yards] [6 x \$125 = \$750] [Pump + \$625] **Total cost \$1,375** 18. How many cubic feet are in 1 cubic yard? **27** [Construction Math -] [This answer can be found in a couple books (such as Carpentry and Building Construction), but this should be a common knowledge question] 19. If materials cost \$1.50 per lineal foot and the labor cost is.50 cents per lineal foot, how much will it cost for 350 lineal feet of material to be installed? **\$700** [Construction Math -] [Examples of Basic Accounting and not in any book] [350 x \$1.50 = \$525] [350 x \$.50 = \$175] [\$525 + \$175 = \$700 Total Cost] 20. The courtyard of a condo complex contains 1,600 sq. feet of area. How many brick pavers will be required to cover the courtyard if each paver is 4\" x 8\"? Allow 5% for waste. **7,560 pavers** [Construction Math -] [You will need to calculate how many square feet are in a single brick paver. Then multiply the number of brick pavers in a square foot by the total area.. Add 5% for waste.] [4" x 8" = 32 square inches Note: One square foot has 144 square inches. (12 x 12)] [144 / 32 = 4.5 brick pavers per square foot] [1600 x 4.5 = 7,200 brick pavers] [7,200 x 1.05 = ]**7,560 brick pavers including waste factor** 21. The earth removed from a hole has a volume of 45 cubic yards and is found to have a compacted volume of 36 cubic yards. What is the percentage of shrinkage for this volume of earth? **20%** [Construction Math -] [The difference between the amount removed and it's compacted volume is 9 cubic yards. ] [When you divide that number (9) into the amount removed (45 cubic yards), the answer is.20% ] [9 / 45 =.2 or 20%] 22. A parking lot is 140 feet wide, and it slopes 1/8th inch per foot. If the highest elevation is 80 feet, what is the lowest elevation? **78.54 feet** [Construction Math -] [For every foot in elevation, there is 1/8th of an inch slope. So how many 1/8ths of an inch exist in 140 feet? However many feet that is, will be subtracted from the high point (80\') to determine the lowest point.] [There is more than one way to arrive at this answer, but here is one solution:] 10. [Convert the 1/8th inch slope to a decimal. 1 divided by 8 =.125] 11. [Find the total amount of slope by multiplying the total width by the slope decimal (140\' x.125 = 17.5 inches of slope)] 12. [Convert elevation to inches (80 x 12 = 960 inches)] 13. [Subtract slope inches from elevation (960 - 17.5 = 942.5 inches of elevation)] 14. [Convert elevation inches back to feet (942.5 / 12 = 78.54 feet)] [Note - 78.54 feet is also the same as 78\' 6.5\"] 23. A brick wall on a residence is 8 1/16" thick, the furring is 3/4", plaster board is 3/8", and the plaster is 1/2". What is the total thickness of the wall? **9 11/16\"** [Construction Math -] [You are adding all the thicknesses together (8 1/16 + 3/4 + 3/8 + 1/2) to get the total thickness of the wall. Find the lowest common denominator to solve: (3/4 = 12/16) (3/8 = 6/16) (1/2 = 8/16) then add them all together: (8 1/16 + 12/16 + 6/16 + 8/16 = 9 11/16)] 24. A mason estimated the following amounts of mortar required for a job -- 5 ½ cubic yards, 11 1/3 cubic yards, and 168 3/4 cubic feet. What is the total amount of mortar required for the job? **23 1/12 cubic yards** [Construction Math -] [For this question you need to add the amounts together, so you will be looking for the lowest common denominator for the fractions. This question has a trick to it, though. You must convert the last amount (168 3/4 cubic feet) into cubic yards by dividing it by 27 (168 3/4 ÷ 27 = 6 1/4). From there you can add them together. (1/2 = 6/12). (1/3 = 4/12). (1/4 = 3/12). The final calculation with everything converted is (5 6/12 + 11 4/12 + 6 3/12 = 23 1/12)] 25. If 2 ¼" high standard bricks are used to lay a wall with 3/8" mortar joints, what is the height of the wall after nine courses? **23 5/8 inches** [Construction Math -] [First you must add the brick height with the mortar joint height to get the total height of each course (2 1/4 + 3/8). Use the lowest common denominator to add (1/4 = 2/8). (2 2/8 + 3/8 = 2 5/8). Then you multiply the total course height by 9 (2 5/8 \* 9 = 23 5/8)] 26. If a set of steps is five risers high, and each rise is 7 ¼",  what is the total rise of the steps? **36 1/4 inches** [Construction Math -] [Multiply the riser height by the number of risers (7 1/4 \* 5 = 36 1/4)] 27. What is the length of a wall consisting of 28 stretchers if each stretcher is 7 ½" and the mortar joint is ½"? **18\'-8\"** [Construction Math -] [First add the stretcher length and the mortar joint to get the total length of each stretcher (7 1/2 + 1/2 = 8). Next multiply the length by the total number of stretchers (8 \* 28 = 224). Now that we know the total length of the wall is 224 inches, we can convert it to feet (224 ÷ 12 = 18 2/3). Two thirds of a foot is 8 inches (2/3 = 8/12). So the total length of the wall is 18\'-8\".] 28. How many risers 7 ½" high are required to construct a flight of concrete steps 3'-1 ½" high? **5 risers** [Construction Math -] [First step is to convert the total height (3\'-1 1/2\") into inches. (3 \* 12 = 36) (36 + 1 1/2 = 37 1/2). The total height is 37 1/2\" and we divide that by the riser height to get the total number of risers (37 1/2 ÷ 7 1/2 = 5).] 29. If a brick mantel is corbeled out 4 ½" in six courses, how much does each course project past the previous course? **3/4\"** [Construction Math -] [We know the mantel extends out 4 1/2\" in six courses, so we need to divide 4 1/2 by 6. The simplest way to solve this is to convert 4 1/2 inches to a decimal (4 1/2 = 4.5). Then using your calculator (4.5 ÷ 6 =.75). Convert back to fraction (.75 = 3/4)] 30. If a story pole is 8'-11 ¼" long and divided into 39 equal spaces, what is the length of each space? **2 3/4\"** [Construction Math -] [The first step is convert the total pole length into inches. (8\' x 12\" = 96\") (96\" + 11 1/4\" = 107 1/4\"). From there you simply need to divide 107 1/4\" by 39. The easiest way to do this is to convert to decimal so you can use your calculator to solve. (107 1/4\" = 107.25\") (107.25\" ÷ 39 = 2.75\"). Convert back to fraction (2.75\" = 2 3/4\"). ] 31. A mason needs to determine if the total cross-sectional area of three pieces of reinforcing steel meet the specifications for a reinforced masonry lintel. The cross-sectional areas of the three pieces are 0.11 sq in, 0.3 sq in, and 1.00 sq in. What is the total cross-sectional area of the three pieces of reinforcing steel? **1.41 square inches** [Construction Math -] [Just add them all together to find their total cross-sectional area (1.00 +.3 +.11 = 1.41)] 32. A cement contractor needs to stake out a foundation on a site that is 125' wide and 200' deep. The plot plan showed that the front of the house (placed along the width of the lot) faced south and was 50' from the lot line. The east side of the house was 28.35' from the lot line and the west side of the house was 36.65' from the lot line. How wide is the front of the house? **60\'** [Construction Math -] [This question includes some information that is irrelevant to solving the problem. By reading the question we know that the front of the house follows the WIDTH of the lot and that it is facing SOUTH. The lot is 125\' wide and we know the east side of the house is 28.35' from the lot line, and the west side is 36.65' from the lot line. With these numbers we can find out the width of the front of the house by adding the distance the sides of the house are from the edge of the lot, and then subtracting that from the total width of the lot. (125\' - (28.35\' + 36.65\') = 60\')] 33. How much should a contractor charge for laying 400 bricks if each brick costs \$0.09 and the contractor wants to make \$0.15 for laying each brick? **\$96** [Construction Math -] [The easiest way to solve this is to add the price per brick with the amount the contractor wants to make on top of the price. (\$0.09 + \$0.15 = \$0.24). Now that we have the final per brick price, we can multiply that by the number of bricks (\$0.24 \* 400 = \$96)] 34. Clay flue lining is sold in 2' lengths. What is the cost of one 2' length if 56' of lining costs \$98? **\$3.50** [Construction Math -] [First find out how many lengths of clay flue lining are in 56\' (56\' ÷ 2\' = 28 lengths). Next divide the total cost by the number of lengths to get your per-length cost (\$98 ÷ 28 = \$3.50)] 35. What is the labor cost of laying 12 ¾ cubic yards of rubble stone if the cost to lay rubble stone is \$9.50 per cubic yard? (Round up to nearest cent) **\$121.13** [Construction Math -] [You need to multiply the cost per cubic yard by the total cubic yards being laid with rubble stone, but first you must convert 12 3/4 cubic yards to a decimal so you can do the rest with your calculator. (12 3/4 = 12.75). (12.75 \* \$9.50 = \$121.125). Round up to nearest cent to get \$121.13] 36. Jerry calculates that 5 cubic yards of sand is needed for a bricklaying job. Because of waste, he adds 5%. How much sand should he order? **5.25 cubic yards** [Construction Math -] [To find 5% of 5 cubic yards, you convert the percentage to a decimal and multiply. (5% = 0.05) (0.05 \* 5 =.25). So he needs to order 5 cubic yards, plus.25 cubic yards extra (5%). 5.25 cubic yards total] 37. It was estimated that 12,000 bricks would be required for a job. An additional 2% were added because of breakage, bats, and salmon brick. How many bricks should be ordered? **12,240** [Construction Math -] [Convert the percentage to a decimal then multiply by the total number of bricks (2% = 0.02). (0.02 \* 12,000 = 240). So 12,000 bricks need to be ordered plus 240 extra (2%). (12,000 + 240 = 12,240)] 38. A large window opening is 72 3/8" by 60 3/8". What is the area of the opening in square feet? Round to 2 decimal places. **30.34 square feet** [Construction Math -] [The first step is to determine the size of the opening in square inches. We want to convert the fractions to decimals to make it easier to multiple the measurements (3/8 =.375) then multiply the measurements (72.375\" \* 60.375\" = 4369.64062 square inches). Then we need to convert square inches to square feet by dividing by 144 (4369.64062 ÷ 144 = 30.34)] [\ ] [(Hint: divide square inches by 144 to get square feet)] 39. A common brick is 8" by 2 ¼" by 3 ¾". What is its volume in cubic inches? **67.5 cubic inches** [Construction Math -] [Simply multiply the three dimensions. You can convert the fractions to decimals to make it easier to input in a calculator (2 1/4\" = 2.25\") (3 3/4\" = 3.75\"). (8\" \* 2.25\" \* 3.75\" = 67.5 cubic inches)] 40. A contractor is laying bricks at a pace of 190 bricks per hour. He has estimated that the wall he is laying bricks for will need a total of about 1350 bricks. Approximately how many hours will it take him to complete the wall? **7.1 hours** [Construction Math -] [Simply divide the total number of bricks (1350) by how many the contractor can lay in an hour (190). 1350/190 = 7.1 hours] 41. Common bricks cost \$11 per hundred bricks. If 14,250 bricks are ordered, how much would they cost? **\$1567.50** [Construction Math -] [Here are two common ways to get the answer: ] [1). Divide the total amount of bricks by 100 (14,250 ÷ 100 = 142.5). Then multiply by \$11 (142.5 \* 11 = 1567.5) giving you a total of \$1567.50. ] [2). Divide \$11 by 100 to get your per-brick price (11 ÷ 100 =.11). Now that you know the cost of each brick, multiply the total number of bricks by 11 cents (14250 \*.11 = 1567.5) giving you a total of \$1567.50.] 42. If it takes 5 bricks to cover 1 square foot of wall space, how many bricks would it take to cover a wall 8\' high by 12\' long? **480** [Construction Math -] [Multiply the dimensions of the wall to get the square footage (8 \* 12 = 96 square feet). Then multiply 96 square feet by 5 bricks per square foot (96 \* 5 = 480).] 43. If a set of steps has 8 risers and the total height of all the steps (total rise) is 56", what is the height of each step? **7\"** [Construction Math -] [Divide the total rise by the number of risers (56 ÷ 8 = 7)] 44. If a brick veneer wall requires 5 bricks to lay up 1 square foot, how many square feet would 587 bricks cover? (Round to nearest whole number) **117** [Construction Math -] [Simply divide total bricks by bricks per square foot (587 ÷ 5 = 117.4), then round to NEAREST whole number = 117] 45. What is the height of one stretcher course of brick if the bricks are 2 3/4" high and the mortar joint is 3/8"? **3 1/8\"** [Construction Math -] [To get the height you must add the brick height with the mortar joint height. (2 3/4 + 3/8). ] [Find the lowest common denominator for the fractions and add them together (3/4 = 6/8) (2 6/8 + 3/8 = 3 1/8)] 46. A homeowner has requested a change order to switch from tile to carpet in the living room.The living room dimensions are 15\' 0\" x 12\' 6\". If tile is \$5.25 per square foot and carpet is \$26 per square yard, determine the approximate amount the homeowner will save. **\$442** [Construction Math -] [Answer: B - Refer to image hint for a detailed explanation] [Show Book Image Hint](https://contractorcourses.com/) 47. A contractor is building a 40\' x 24\' single story house with a 6/12 straight gable roof and 96\" from sole plate to top plate. How many 4\' x 8\' sheets of wall sheathing are required? Do not deduct openings or add waste. **37** [Construction Math -] [How they figure it: ] [The sheets of wall sheathing are 4 feet wide, so if you add the length of the perimeter (40 + 40 + 24 + 24) you get 128 linear feet. If the sheets are 4 feet wide, you can divide 128 by 4 to get 32. ] [Now that we know it will take 32 sheets to border the bottom, we can see that the distance from the sole plate to the top plate is 96 inches (or 8 feet). Since the sheets are also 8 feet tall, we know that the 32 sheets are also tall enough to cover the walls. All that is left is to calculate how many sheets for the gabled roof.] [The 6/12 pitch would give us a gable peak of 72", or 6'. (6/12 means that for every 12\' in length, the rise would go up 6\'. Since it is a peak of a triangular gable that is 24\' wide, you would cut that width in half giving you 12\' in length and thus a gable peak of 6\')] [ 6' x 24' = 144 sq. ft.144 sq. ft. / 32 sq. ft. is 4.5 pieces (Since this is a square foot calculation, it would cover both ends of the building. ] [ Of course, you have to round up the 4.5 to 5 pieces. 32 + 5 = 37]