Question

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?

Answer 1

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

$1 + 5 + x1 = 1 + 5 + x2$

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

But now we have to be careful, because

$5 + x + y = x + x + y$

Simplifying we can get the value of x:

$x = 5$

Now, substituting back in, we get

$1 + 5 + 5 = 5 + 5 + y \\ y = 1$

So, the sum of all vertexes is equal to

$2 \times 1 + 3 \times 5 = 17$