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a mosaic table top has triangular and rectangular peices for every 8 rectangular pieces there are 12 triangular pieces there are a total of 80 pieces how many of each shape are used

User Jpoppe
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1 Answer

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Let's use "r" to represent the number of rectangular pieces and "t" to represent the number of triangular pieces.

From the problem, we know that for every 8 rectangular pieces, there are 12 triangular pieces. This can be written as:

12/8 = 3/2

So for every 2/3 of a triangular piece, there is 1 rectangular piece.

We also know that there are a total of 80 pieces. So we can set up an equation:

r + t = 80

We can use the ratio of 2/3 to set up another equation:

r = (2/3)t

Now we can substitute the second equation into the first equation and solve for t:

(2/3)t + t = 80
(5/3)t = 80
t = (3/5) * 80
t = 48

So there are 48 triangular pieces. To find the number of rectangular pieces, we can use the second equation:

r = (2/3)t
r = (2/3) * 48
r = 32

So there are 32 rectangular pieces.

Therefore, there are 48 triangular pieces and 32 rectangular pieces used in the mosaic table top
User AJ Poulter
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