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In the diagram, there is an object with 6 triangular faces. On each corner there is a number (two are shown). The sum of the numbers on the corners of each triangle is the same. What is the sum of all 5 numbers?

In the diagram there is an object with 6 triangular faces On each corner there is a number two are shown The sum of the numbers on the corners of each triangle class=

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Answer:

17

Step-by-step explanation:

Let the two "middle" vertexes be x1 and x2, and let the "lower" vertex be y. We know that

[tex]1 + 5 + x1 = 1 + 5 + x2[/tex]

Therefore x1=x2. We'll call that value just x.

But now we have to be careful, because

[tex]5 + x + y = x + x + y[/tex]

Simplifying we can get the value of x:

[tex]x = 5[/tex]

Now, substituting back in, we get

[tex]1 + 5 + 5 = 5 + 5 + y \\ y = 1[/tex]

So, the sum of all vertexes is equal to

[tex]2 \times 1 + 3 \times 5 = 17[/tex]

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