5.5.5 Home Improvement Project
Let’s take a look at a real-world problem that pulls in many of the topics we have studied so far, like units of measurement, the basic operations, and rounding.
On a home improvement store’s website, the following instructions were given for calculating how many rolls of wallpaper are needed to decorate a room.
Calculate the number of rolls you will need, using the method outlined below.
- Step 1: A standard roll of wallpaper is approximately 10.5 m (33 ft) long and 530 mm (1 ft 9 in) wide. If you measure the height of the walls from the baseboard (skirting board) to the ceiling, you can determine how many strips of paper you can cut from a standard roll—four strips are about average.
- Step 2: Measure around the room (ignoring doors and windows) to work out how many roll widths you need to cover the walls. Divide this figure by the number of strips you can cut from one roll to calculate how many rolls you need to buy. Make a small allowance for waste.
Activity: Following the Instructions
(a) Read through the directions above. Write down the important information. What did you do to make sense of these instructions?
Try drawing a sketch, and think through the steps you would take to apply new wall paper in your kitchen. Thinking about the math cycle from Unit 4 may help as well.
(a) This is how Tony, a student, tackled the problem. His notes are given below.
- I read all the instructions through first of all to get an overall idea of what I would need to do. Then I went back and highlighted the key bits of information—the dimensions of the roll of wallpaper and the instructions for what I needed to measure.
I wasn’t sure what “ignoring doors and windows” meantin the instructions for measuring round the room. Did it mean you shouldn’t measure the part of the wall occupied by the door and window, or that you should measure the width and length of the room as though there wasn’t a door and window there? I discussed this with a friend and decided to measure as though there wasn’t a door and window, since that would overestimate the amount required and I didn’t want to end up with too few rolls of wallpaper.
- Then, I concentrated on the calculations. There are three calculations:
- Working out how many strips of paper you can cut from a standard roll.
- Working out how many roll widths there are round the room.
- Calculating how many rolls are needed.
- I used the measurements to sketch out a diagram so that I could visualize the problem more easily as well. My room measured 3.2 m by 4 m, and the baseboard to ceiling height was 2.34 m. So, the distance round the room was .
- For the second calculation, I considered a simpler problem first. Say a wall that was 10 m long, and a roll of paper that was 0.5 m wide—that helped me to see that I needed to divide the length of the wall by the width of the roll, since the question was “how many widths are there along the wall?”.
(b) Using your own measurements for a room (or assume the room measures 3.2 m by 4 m and the height of the walls is 2.34 m), work out how many rolls will be needed.
(b) [ 10.5 m is equal to 1050 cm since there are 100 cm in 1 m. ] The first calculation is to work out how many lots of the height (2.34 m) you can get from a roll of wallpaper that is 10.5 m long (information provided at the website in Step 1).
Therefore, number of strips of wallpaper from one roll =
(Note that all the dimensions have been converted to the same units. The wavy equals sign means “approximately equals to.”)
You might be tempted to round this up to five, but in this real-world problem, we must round down to four, as the roll of wallpaper is not long enough to but cut into five strips each of length 234 cm.
So, you will only be able to get four strips from each roll.
Next, you need to work out how many strips are required to cover the room. If you already have a roll of wallpaper, you could count how many strips you’ll need by measuring along the wall with the roll of paper.
[ ] If you don’t have any wallpaper, you can calculate how many 53 cm (given at the website in Step 1) wide strips will fit in to 14.4 m. So, the total number of strips needed is . Rounding this up, to make sure we have enough paper, gives 28 strips altogether. As there are four strips in each roll, so rolls will be needed. This will allow for some wastage, because paper is not put over the doors or windows. However, if the paper has a large pattern that needs matching up, it might be worth buying an extra roll to be on the safe side. If money is tight, go with the seven rolls, and just be extra careful when hanging them up.
Well done for completing the problem—it had a lot of separate steps to get to the final answer.
Now it’s time to check back over the topics covered in this unit by completing the self-check section.