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All triangles have the same value, and all circles have the same value. What is the sum of two circles?

 

\(\begin{align*} \Delta + \bigcirc + \Delta + \bigcirc + \Delta + \bigcirc + \Delta + \Delta&= 21\\ \bigcirc + \Delta+\bigcirc+\Delta+\bigcirc + \Delta + \bigcirc + \bigcirc &= 16\\ \bigcirc + \bigcirc &= \ \, ? \end{align*}\)

 Feb 11, 2021
 #1
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+1

5t + 3c = 21     Or  multiply by -3  to get

  -15t -9c = -63

3t + 5c = 16          Multiply by 5 to get   
15 t + 25c = 80         Add eq 2 an 4 to get

16c = 17         Divide by 8

2c = 17/8

 Feb 11, 2021
 #2
avatar+120129 
+1

Let  the triangles  = x

Let  the circles  = y

 

So  we  have

 

5x + 3y   =  21   mult through by -3  ⇒  -15 x  -  9y   =  -63

3x +  5y  =  16    mult through by 5  ⇒   15x   +  25y  =  80      add these

 

 

-16y  =  -17

y  =  -17/-16 = 17/16

 

So

 

2y  =    34 / 16   =  17 / 8 

 

 

cool cool cool

 Feb 11, 2021
 #3
avatar+8 
-1

Thanks so much!

 

It was right, but i tped it in wrong... so i got it wrong. But thanks!

AydenFilmoreismybro  Feb 11, 2021

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