Math CentralQuandaries & Queries


Question from Susan, a parent:

What size rectangular table will we need to put 230- 2" X 3.5" escort cards on for my daughter's wedding reception with a spacing of .5 inch between them on all sides? Thanks so much for your help

Hi Susan,

If you imagine each card has an extra 1/4 inch border all the way around this gives 1/2 inch of spacing between the cards on all sides but only 1/4 inch at the edge of the array of cards. We can deal with that later so I am going to assume the cards are 2.5 inches by 4 inches. The area of each card is then 2.5 × 4 = 10 square inches. There are 230 cards so you need a minimum of 2300 square inches of space.

A table that is 4 feet square (48 inches square) has an area of 48 × 48 = 2304 square inches, but it's not quite that easy. Each card is 4 inches long and 48/4 = 12 so you can place 12 cards along the edge of the table. Each card is 2.5 inches wide and 48/2.5 = 19.2 so you can put 19 rows of 12 cards on the table. 19 × 12 = 228 cards. Oh so close. (Maybe the Smiths from Seattle and the Jones from Denver won't be able to come and you will be ok.)

This is the calculation you are going to need to perform. Measure a candidate table in inches, for example a table might be 78 inches by 30 inches. Find the area of the table. For the 78 by 30 inch table 78 × 30 = 2340 square inches. If the area is less than 2300 square inches the table is too small. If the area is large enough then arrange the cards.

If you put the long side of the cards along the long side of the table then 78/4 = 19.5 so you can get 19 cards along the length. In the other direction 30/2.5 = 12 so you can display 12 × 19 = 228 cards again, as with the 4 foot square table.

If you put the long side of the cards along the short side of the table then 30/4 = 7.5 so you can get 7 cards along the width of the table. In the other direction 78/2.5 = 31.2 so you can display 7 × 31 = 217 cards.

Measure some candidate tables and perform this calculation to see which one will work.

Good luck with this,

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