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


 Jun 12, 2021
 #1
avatar+181 
+2

Let the triangle = $x$ and the circle = $y$.

 

Thus, the two equations are

 

$3x + 2y = 21$ and $3y + 2x = 19$. 

 

Since we want to find $y$, we multiply the second equation by $\frac{3}{2}$ to get $\frac{9y}{2} + 3x = \frac{57}{2}$. 

 

Subtracting the second and first equations gives $\frac{5y}{2} = \frac{15}{2}$

 

Thus, $y = 3$, which is the value of the circle. Can you solve it from here? 

 Jun 12, 2021
 #2
avatar+114485 
+1

This question may have been asked by a child who has never used algebra.

It is easier to use algebra for a person who knows how BUT here is how another way to do it.

 

the first one has             2 circles, 2 trangles and another triangle and it adds to 21

the second one has       2 circles, 2 trangles and another circle and it adds to 19

 

So the triangle must be bigger than the circle by 2.  (because that is the only difference)

 

So if I replace each of the triangles in the second one with  a circle plus 2 more I get

 

5 circles + 2+2 = 19

If 5 circles plus 4 more equals 19 then

5 circles must equal 15

so one circle must be 3       (because 3+3+3+3+3=15)

 Jun 13, 2021

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