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




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

 Nov 18, 2020
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We can label the traingles as $t$ and the circles as $c$ to get

$5t+3c=21$

$5c+3t=16$

as our system of equations. Since I am kind of sleepy today, I plugged this into Wolfram|Alpha and got

$t=\frac{57}{16}$

$c=\frac{17}{16}$

so, 

$2c=\frac{34}{16}=\frac{17}{8}$.

 Nov 18, 2020
edited by MathzSolver111  Nov 18, 2020

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