MATHEMATICAL EXCURSIONS A do-it-yourselfer is a person that does projects around the home without using professional trades people like carpenters, plumbers, electricians, landscapers, or other handymen. In a doit-your self project, only materials and tools are purchased and no labor costs are paid. Thus, money is saved. Besides, completing the project gives most do-it-yourselfers a sense of pride in accomplishing something that they may not have done before. In any do-it-yourself project, you must first get information on how to do the project. This information can be obtained from books, pamphlets, internet sites, and experts at your local home improvement store. Once you decide you can do a project, you must find out what tools and materials are needed. The mathematics involved in the project is centered around estimating the materials needed and determining the cost of the project. The estimation phase may require making sketches and using the measurement geometry formulas of Chapter 3. In this section, we will look at some projects you might attempt and use prices for tools and materials that you might find at a local building supply center or home improvement store such as Home Depot or Lowe s. (Note: All prices and sales tax rates used in this section are from retail stores in Pleasanton, California, in October of 2005. Prices in your area may vary.) Project : Replacing a Kitchen Faucet After investigating how to replace a kitchen faucet, you find that math will only be used to determine the cost of the project. You make a list of tools and materials noting what you already have and the price of items you need to purchase. Pliers 0 Crescent Wrench $.98 Philips Screwdriver Flathead Screwdriver MATERIALS AMOUNT HAVE? PRICE Kitchen Faucet $99.99 ½" FIP 3 /8" OD Stop Valve 2 $3.98 ea 20" Faucet Connector Hose 2 $4.98 ea Tub of Plumber s Putty $.97 Teflon Pipe Tape page 48
To determine the cost, find the total of all the items in the list making sure to add the 8.75% sales tax. Items =.98 + 99.99 + 2(3.98) + 2(4.98) +.97 = $3.86 Tax = 0.0875(3.86) = $.54 Total = $3.86 + $.54 = $43.40 Project 2: Building a Book Shelf Before building the book shelf, you make a sketch of the shelf including the desired dimensions and decide on the materials to use. (Note: Because of package sizes and dimensions of materials, if there are fractional amounts needed you should purchase the next whole amount.) 6' 4' ' Wood: The clear pine you need for the shelves comes in " 2" 8' boards. Sides: The sides are 6 ft tall so each side will take a board. Thus, 2 boards are needed. Shelves, Top, Bottom: Each of the five pieces are 4 ft long so it will take three 8 ft boards, cut in half. Back: The back is 4' 6'. Since the plywood comes in 4' 8' sheets, you will need one sheet. The excess material as found in all three parts is a common result of most do-it-yourself projects. Do-it-yourselfers just keep the excess amounts for other projects. Stain and Finish: To determine the amount of stain and clear gloss finish you need, find the surface area of all the rectangular shaped boards in the shelf using the formula, area equals length time width, A = lw. Area: top of 5 horizontal boards: 5 4 = 20 bottom of 5 horizontal boards: 5 4 = 20 inside and outside of sides: 4 6 = 24 inside back: 6 4 = 24 Total = 88 sq ft Since the coverage of one quart of the stain and gloss finish is 25 sq ft, one quart of each is enough. With those computations completed, here is the tool and material list for the project. page 49
Hammer Hand Saw $9.98 Cordless Drill and Bit Philips Screwdriver Square $6.97 Paint Brushes MATERIALS AMOUNT HAVE? PRICE " 2" 8' Clear Pine 5 boards $2.48 ea 4' 8' sheet ½" Plywood sheet $9.99 2" Wood Screws lb $4.32 Wood Glue Sandpaper Wood Stain qt $8.97 Gloss Finish qt $7.98 Wood Filler tube $.97 To determine the cost find the total of all the items in the list and add the 8.75% sales tax. Items = 9.98 + 6.97 + 5(2.48) + 9.99 + 4.32 + 8.97 + 7.98+.97 = $32.58 Tax = 0.0875($32.58) = $.60 Total = $32.58 + $.60 = $44.8 Project 3: Constructing a Concrete Walkway You decide to construct a 4 inch thick concrete walkway with dimensions shown below. 3.5' 6' 2.5' 8' 4.5' 3.5' The do-it-yourself book states that you must determine the amount of wood framing for the concrete form, the gravel, wire mesh, and bags of concrete-mix for the walkway. Framing: The frame goes around the perimeter of the walkway. P = 6 + 8 + 3.5 + 4.5 + 2.5 + 3.5 = 48 ft The 2" 4" framing boards come in 8 ft lengths. So, you will need six of them. page 50
Gravel: According to the do-it-yourself book, you need 2 inches of base gravel below the bottom of the concrete form. Since the gravel is sold by the yard (yd 3 ) in one-half yard increments, find the volume of the gravel in cubic yards. The formula for the volume of a rectangular solid is the product of its length, width, and height (V = lwh). Separating the walkway into two rectangular regions, one 6 ft by 3.5 ft by 2 in (/6 ft) and the other 4.5 ft by 3.5 ft by /6 ft, we get the following. V = 6 35. + 45. 35. 6 6 9. 333+ 2. 625 3. 958 ft note: yd = 27 ft 3 3 ( ) ( ) 3 2 yd The gravel is sold in 2 cubic yard increments. Wire mesh: Since the wire mesh has a width of 3.5 ft and comes in 7 ft lengths, you need an amount to cover the bottom of the frame. Length = 6 + 4.5 = 20.5 2 ft. Thus, you need 3 sections of wire mesh. Concrete-mix: Since the concrete-mix comes in 2/3 cu ft bags, find the volume of the mix needed to fill the 4 inch (/3 ft) deep concrete forms. Using the techniques we used for the gravel, we get the following. V = 6 35. + 45. 35. 4 4 = 4 + 3. 9375 = 7. 9375 8 ft 3 2 3 Number of bags of concrete-mix = 8 = 8 = 27 3 2 With these estimates, the cost for the tools and material to complete the walkway can be determined. Wheelbarrow Hammer, Saw Finish Trowel $8.49 Concrete Edger $3.97 Wire Cutters, Level Concrete Mixer (rental) $42.00 per day page 5
2 /3 ft 3 Bag Concrete-Mix 27 bags $3.98 Base Gravel ½ yd $43.00 per yd 3 3.5' 7' Wire Mesh 3 sections $4.98 ea 2" 4" 8' Fir 6 boards $2.75 ea 2" Wood Stakes bundle $8.33 2 ½" Galvanized Nails lb $2.3 per lb To determine the cost find the total of all the taxable items in the list, add the 8.75% sales tax, and add the concrete mixer rental charge. Items = 8.49 + 3.97 + 27(3.98) + 0.5(43.00) + 3(4.98) + 6(2.75) + 8.33 + 2.3 = $83.32 Tax = 0.0875(83.32) = $6.04 Rental = $42.00 Total = $83.32 + $6.04 + 42.00 = $24.36 The projects outlined in the exercises that follow, will give you some experience in planning other do-it-yourself projects. Remember, in the planning stage, you must first get information on how to do the project, you must decide if you can do the project, find out what tools and materials are needed, and estimate the cost of the project. Have fun being a do-it-yourselfer. Exercises. What factors must be considered before starting a do-it-yourself project? 2. What are the basic steps in determining the cost of a do-it-yourself project? 3. What do you have to do when measurement estimates of materials have fractional amounts? In Problems 4 7, use an 8.75% sales tax rate in determining the cost of each project. 4. Painting a Shed: A sketch of a shed and its dimensions are given below. You are going to give all exterior walls a coat of primer and a coat of latex paint that each having a coverage of 350 sq ft per gallon. Determine the amount of paint needed and the cost of the project using the prices given in the charts below. 2' 8' 2' 0' page 52
Paint Brushes Paint Roller/Tray $7.97 Sand Paper Exterior Primer Paint? $7.97 per gal Exterior Latex Paint? $9.97 per gal 0. oz Latex Calking 2 $.97 ea 5. Making Planters: You are building two containers to grow herbs and vegetables as sketched below. You are filling the planters with a 50-50 mix of dirt and bags of Super Garden Soil so that the mixture in the planters is.5 feet deep. Determine the number of 2" 6" 8' pressure treated boards and the number of.5 cu ft bags of Garden Soil that are needed for the planters. If you have all the tools necessary for the project, what is the cost of the materials using the prices given in the chart below. 2' 8' 4' 2" 6" 8' Pressure Treated Wood? $7.97 ea 3 ½" Galvanized Nails 2 lbs $2.3 per lb.5 ft 3 Garden Soil? $4.27 per bag 6. Tiling a Bathroom Floor: You are retiling a bathroom floor (sketched below) with 2 inch square self adhesive vinyl tiles. If the tiles come in boxes that hold 20 tiles, how many boxes should you buy and what is the cost for the project? 3' 8.5'.5' 2' Vinyl Tile (box of 20)? $9.60 Knife and Blades $5.99 page 53
7. Laying Sod: You are going to replace the weeds in your back yard with sod. The area to be sodded consists of a rectangle, a right triangle, and semi-circle as sketched below. Assume the ground has been prepared properly and all preliminary steps have been completed. All you have to do is mix in Turf Soil Amendment into the area at the rate of.5 cu ft per 20 sq ft of area and lay the sod according to the do-it-yourself directions. The directions state that because of cutting you will need four extra rolls of sod. If you have all the necessary tools, how much soil amendment and sod is needed and how much will this phase of the project cost? 38' 2' 2' 20'.5 ft 3 Soil Amendment? $3.98 per bag 5 ft 2 roll of Sod? $.70 ea plus $45 delivery 8. The fertilizer recommended for the lawn in Problem 7 has a coverage of 20 lbs for 6000 square feet. How many pounds of fertilizer should you use to fertilize the lawn? If you fertilize the lawn 4 times per year, how many 20 lb bags of fertilizer will you buy in a year? 9. Your Own Project: Plan your own do-it-yourself project. Find information for doing the project, make sketches if necessary, determine the tools and materials needed, find prices, and estimate the cost of the project. page 54