Real-Life Math
You are a bookbinder. You work in a small, independent hand bindery. You've been asked to make a wedding album for a friend. He gives you the measurements and the types of materials he prefers. He does not have a lot of money, so he asks you to try to minimize any waste.
There are 4 items that you need in order to make the album: a cover (made up of 2 boards), 2 pastedowns of heavy vellum (a fine leather parchment paper), 2 flyleaves of heavy vellum and fine vellum sheets to be folded to make the pages.
Your friend has specified the album pages to be 11 1/2" x 13 1/2" to accommodate the photos he plans to put in it.
You begin the job by ordering fine vellum paper -- ivory with a tinge of pink for warmth. The best price on this particular vellum is from a supplier who has 18 pieces of 30" x 48" left over from another project. He will sell them to you at a fraction of their original cost.
You find two 14" x 36" pieces of the same color vellum in a heavier gauge at another supplier who will have them delivered to you. These will work well for the pastedowns and the flyleaves, or endpapers.
You buy the best quality cover boards your friend can afford. They're 11 5/8" by 13 5/8". The cover boards are 1/8" larger in both width and length than the pages so that they will protect the pages without being too large.
The front cover board and the back cover boards each are (11 1/2" + 1/8" = 11 5/8") in width and (13 1/2" + 1/8" = 13 5/8") in height. You decide on a white matte leather skin for the cover on which you can tool their names and the date of their wedding along with some ornate scrollwork.
Your job now is to figure out if you have enough supplies and how many pages the album will be. Begin by planning how you will cut the 2 pieces of heavy-gauge vellum to make the pastedowns and the flyleaves (endpapers), then go on to calculate how you will cut and fold the 18 pieces to make pages.
Hint: Draw a diagram of a rectangle representing the size of the 2 heavy pieces of vellum and decide what you need to make from them. Use dotted lines to represent the dimensions of the items you need to cut from these 2 sheets. Try to make the items fit in with as little waste as possible (like cutting cookies from a piece of rolled-out dough).
Then draw another rectangle representing the 18 pieces of fine vellum that will make up the pages of your album. Remember that you want to cut sheets to be folded in half to form the pages of your album. The fold will be attached to the spine of the album.