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The Tasty as Pi Bakery has two locations! Each location offers the same flavors. Both locations display one pie of each flavor in a rectangle.

The downtown location has \(4\) rows in its display. The uptown location has \(6\) rows in its display. If one of the locations has a square display, how many pies are in each of the other location's rows?
 

 Jun 20, 2023
 #1
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There are two possible cases:

Case 1: The downtown location has a square display. In this case, the number of pies in the downtown location is 44 = 16. The number of pies in the uptown location is 66 = 36. Therefore, there are 6 pies in each row of the uptown location.

Case 2: The uptown location has a square display. In this case, the number of pies in the uptown location is 66 = 36. The number of pies in the downtown location is 44 = 16. Therefore, there are 4 pies in each row of the downtown location.

We cannot know which location has the square display, so both cases are possible. Therefore, the answer is either 6 or 4.

 Jun 20, 2023
 #5
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The bakery that has a square display must have an even number of pies, because a square has an even number of sides. Since the downtown location has 4 rows, the uptown location must have the square display. This means that the uptown location has a total of 6×6=36 pies. Therefore, each row in the uptown location has 36/6=6 pies.

The downtown location must have 4×6=24 pies total. Since each row in the uptown location has 6 pies, each row in the downtown location must have 24/4=6 pies.

Therefore, the answer is 6 pies.

Guest Jun 21, 2023
 #2
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The Tasty as Pi Bakery has two locations! Each location offers the same flavors. Both locations display one pie of each flavor in a rectangle.  

The downtown location has 4 rows in its display. The uptown location has 6 rows in its display. If one of the locations has a square display, how many pies are in each of the other location's rows?  

 

 

1.  Each location offers the same flavors.  

2.  Both locations display one pie of each flavor. 

3.  So, both locations display the same number of pies. 

4.  Both locations displays are rectangles.  

5.  One location has a square display.  

 

If the downtown location has the square display,  

then it has a four by four display, total 16 pies.  

Then, the uptown display must have the 6 rows. 

Have to fit 16 pies into 6 rows?  It doesn't come  

out even, so this one cannot be a rectangle..  

 

Leave that for now, while we look at the other option.  

 

If the uptown location has the square display,  

then it has a six by six display, total 36 pies.  

Then the downtown display is the one with 4 rows. 

If they put 9 pies in each row, that's 36 pies, too. 

 

I think this makes a case for each location displaying 36 pies each.  

.

 Jun 20, 2023
 #4
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Ruh Roh!  A second, more careful reading of the

problem reveals that I had misread it the first time.  

 

It doesn't ask for the total number of pies at each location.  

It asks for the number of pies in each row at each location.  

 

My reasoning works the same way, and my amended answer  

is:   

 

The uptown location has 6 pies in each row  (6 x 6 = 36 total pies).  

The downtown location has 9 pies in each row  (4 x 9 = 36 total pies).  

 

This way, both locations have a rectangular display    

(a square is a special case of a rectangle) and both    

locations show every pie, which was a stipulation.   

.

Bosco  Jun 21, 2023
 #3
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Let's denote the number of pies in each row at the downtown location as "x" and the number of pies in each row at the uptown location as "y."

We are given that the downtown location has 4 rows, and the uptown location has 6 rows. Additionally, we know that one of the locations has a square display, which means that the number of pies in each row is equal to the number of rows.

If the downtown location has a square display, then the number of pies in each row at the downtown location is 4 (since there are 4 rows).

Therefore, x = 4.

To find the number of pies in each row at the uptown location, we can set up a proportion using the given information:

4 (pies in each row at the downtown location) / 6 (number of rows at the uptown location) = y (pies in each row at the uptown location) / 6 (number of rows at the uptown location)

Simplifying the proportion:

4/6 = y/6

Cross-multiplying:

4 * 6 = 6 * y

24 = 6y

Dividing both sides by 6:

24/6 = y

4 = y

Therefore, if the downtown location has a square display with 4 rows, then the uptown location will have 4 pies in each of its 6 rows.

 Jun 21, 2023

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