Can someone solve with a system of equations and show work?
1 answer:
Answer:
1
Step-by-step explanation:
Label the points as in the attachment. Then we have ...
- P = (a+b)/2
- Q = (b+c)/2
- R = (c+d)/2
- S = (d+e)/2
- T = (e+a)/2
We can form the sum P + R + T and we get ...
P +R +T = (a+b)/2 +(c+d)/2 +(e+a)/2 = a +(b +c +d +e)/2
We can form the sum Q + S and we get ...
Q + S = (b+c)/2 +(d+e)/2 = (b +c +d +e)/2
Subtracting the latter sum from the former one gives ...
P +R +T -(Q +S) = a +(b +c +d +e)/2 -(b +c +d +e)/2 = a
__
So, the value picked by the person with the average "6" was ...
(7 +1 +5) -(9 +3) = 13 -12 = 1
The person with average "6" picked 1.
_____
The system of equations written in matrix form is shown in the second attachment. The inverse of the coefficient matrix is shown in the third attachment. That is where the sum shown above came from.
__
The rest of the picked numbers are ...
P = 2, b = 13, Q = 14, c = 5, R = 6, d = -3, S = -2, e = 9, T = 10
You might be interested in
Step one:
ALWAYS set equation equal to zero, which in this case has already been done for us.
Step two:
Figure out what formula you need to use in order to solve in this case I'd use the Quadratic formula.
a=1
b=9
c=2
Quadratic formula:
Then you would plug in the information.
The solve for what is underneath the square root ONLY.
Since you cannot solve this any further, your final two answers are...
ALWAYS set equation equal to zero, which in this case has already been done for us.
Step two:
Figure out what formula you need to use in order to solve in this case I'd use the Quadratic formula.
a=1
b=9
c=2
Quadratic formula:
Then you would plug in the information.
The solve for what is underneath the square root ONLY.
Since you cannot solve this any further, your final two answers are...