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# A box contains a collection of triangular and square tiles. There are

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Math Expert
Joined: 02 Sep 2009
Posts: 55277
A box contains a collection of triangular and square tiles. There are  [#permalink]

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25 Apr 2019, 01:53
00:00

Difficulty:

15% (low)

Question Stats:

77% (01:38) correct 23% (01:51) wrong based on 31 sessions

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A box contains a collection of triangular and square tiles. There are 25 tiles in the box, containing 84 edges total. How many square tiles are there in the box?

(A) 3
(B) 5
(C) 7
(D) 9
(E) 11

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Re: A box contains a collection of triangular and square tiles. There are  [#permalink]

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25 Apr 2019, 06:40
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Top Contributor
Bunuel wrote:
A box contains a collection of triangular and square tiles. There are 25 tiles in the box, containing 84 edges total. How many square tiles are there in the box?

(A) 3
(B) 5
(C) 7
(D) 9
(E) 11

Let T = the number of triangular tiles in the box
Let S = the number of square tiles in the box

So, 3T = the number of edges for all T triangles
And, 4S = the number of edges for all S squares

There are 25 tiles in the box. . .
We can write: T + S = 25

. . . containing 84 edges total
We can write: 3T + 4S = 84

How many square tiles are there in the box?
In other words, what is the value of S?

We have:
T + S = 25
3T + 4S = 84

Take TOP equation and multiply both sides by 3 to get:
3T + 3S = 75
3T + 4S = 84

SUBTRACT the bottom equation from the top equation to get: -S = -9
Solve: S = 9

Cheers,
Brent
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Re: A box contains a collection of triangular and square tiles. There are  [#permalink]

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27 Apr 2019, 03:59
Bunuel wrote:
A box contains a collection of triangular and square tiles. There are 25 tiles in the box, containing 84 edges total. How many square tiles are there in the box?

(A) 3
(B) 5
(C) 7
(D) 9
(E) 11

given s+t= 25
and 3t+4s= 84
solve
s= 75-84 ; 9
IMO D
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Re: A box contains a collection of triangular and square tiles. There are   [#permalink] 27 Apr 2019, 03:59
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