Real-Life Math
In the upholstery business, supplies must be ordered and fabrics must be cut and measured. Of course, you always try to order just as much as you need and measure the fabric correctly the first time.
It's important when using expensive materials (usually the fabric on the outside of upholstery) to cut the right size needed for the pattern.
If you miscalculate and cut a pattern that is too small to cover a boat top, you're out of luck. You'll simply have to remake the top out of a new piece of material.
But cutting a piece of material too small isn't the only problem. You also can't afford to purchase far more material than is necessary to complete a job.
Part A
This afternoon, you're working on 4 cushions to go with an antique bed that you've just refurbished. You have extra scraps of silk left over from the bed, and because it's such an expensive fabric, you don't want it to go to waste.
You want to make 3 throw cushions, which will each take 15 inches by 15 inches of fabric. You have a scrap of deep red silk that is 1 yard by 1 yard. Will you have enough to make the pillows from this material?
Hint: rather than working with numbers, upholsterers often work with patterns.
Part B
You also want to make a bolster cushion -- the cylindrical cushion that props up under a person's neck for reading in bed. It is made of 2 round end pieces that are attached to 1 rectangular piece that forms the cylinder part of the cushion. The diameter of 1 end of the cushion is 3.5 inches.
How big will you have to make the 2 circles for the ends of the cylindrical cushion? You want the cushion to be 12 inches long. How big do you want the central piece of fabric to be?