Question

Need help with troiminos.. REALLY BAD. Medal and fan.

(picutre for an example of what i need help on.)

Answer 1

:?

Answer 2

@mathstudent55 Do you have any idea?

Answer 3

No. I'm trying but can't figure it out.

Answer 4

Ok, I figured it out.

Answer 5

In each triomino, there is a rule of how to go from the three numbers in the vertices of the triangle to the number in the center. The rule for all four triominos is the same.

Answer 6

The number in the center is a linear combination of the numbers in the vertices.

Answer 7

Let's call the numbers in the vertices P, Q, and R, and the number in the center C.

Answer 8

Multiply P by a number, Q by another number, and C by another number. Then add these products together, and the result is C.

Answer 9

That is the rule. The job is to use the three given triominos to find the rule. Then you can apply the rule tot he 4th triomino,.

Answer 10

You will end up with a system of three equations in three variables. Once you solve it, you'll know the multipliers of P, Q, and R, and you'll know the rule. Then you apply the rule to the 4th triomino to find its C.

Answer 11

6a - 3b + 4c = 5
-4a + 7b +3c = -14
2a - 8b + 9c = 1

Solve this system for a, b, and c.

Once you know a, b, and c, to find the missing number,
use the information form the 4th triomino:

5a + 8b - 3c = ?
Substitute the values of a, b, and c in the expression above to find the missing number.