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Pat has two sheets of large, square stamps. One sheet consists of  9 stamps arranged in a 3-by-3 square. (That's 3 stamps by 3 stamps, not 3 inches by 3 inches.) The other sheet consists of 100 stamps arranged in a 10-by-10 square. The stamps on each sheet are separated by perforated creases. All the stamps on both sheets are the same shape and size.

 

The total length of the creases on the 3-by-3 sheet is  18 inches.

 

How many inches of creases does the 10-by-10 sheet have?

 Nov 27, 2020
 #1
avatar+40 
+3

If the 3x3 and 10x10 square have the same proportions meaning they have same sized stamps and same sized creases, it's just a proportionality problem so take the area of the 10x10 over the 3x3 100/19. The multiply that by the length of the creases on the 3x3 sheet to get 200.

(Correct me if I'm wrong)

 Nov 27, 2020
 #2
avatar+116126 
+2

This is similar to  the toothpick problem

 

Number of perforations in the  3 x 3 sheet 

 

Number of   stamps in  each row  *  ( 3-1) rows  +    Number  of stamps in each column * ( 3 - 1) columns  =

 

(3) (3-1)  +  (3) ( 3-1)  =

 

3(2)   +  3 (2)  = 

 

12

 

So   each perforation  =   18 inches  / 12 =   1.5  in   

 

Using the  same reasoning  applied to  the  10 x 10  sheet

 

(10 (10 - 1)  +  10 (10 - 1)  =

 

10 (9)    +   10 (9)   = 

 

90  +  90   =   180  perforations

 

180 *  1.5   =

 

270 inches 

 

 

cool cool cool

 Nov 27, 2020
 #3
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+1

There are 4 creases in the 3x3   two vertical two horizontal

  18/4 = 4.5 inches per crease

     each stam is thus    4.5 in / 3 stamp = 1.5 in per stamp

 

In a 10 x 10 there are 18 creases

10 stamps x 1.5 in/stamp x 18 = 270 inches total

 Nov 27, 2020

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