Answer:
A third place vote is worth 1 point
Step-by-step explanation:
Let the number of points for a first place vote be x, number of points for a second place vote be y and the number of points for a third place vote be z.
So, by multiplying the number of points by the number of what the point is worth and adding all together, we shall have the total points;
Hence, we have the following equation systems;
23x + 5y + z = 131
5x + 17y + 4z = 80
x + 5y + 15z = 35
These are the three equations we need to solve simultaneously to get the value of z
From equation 3, x = 35 -5y -15z
Insert this into the first two equations;
23 ( 35 -5y -15z) + 5y + z = 131
5(35-5y-15z) + 17y + 4z = 80
805 - 115y -345z + 5y + z = 131
805-131 = 115y + 345z -5y - z
674 = 110y + 344z ••••••••••(*)
The second equation now becomes the following;
5(35-5y-15z) + 17y + 4z = 80
175 -25y -75z + 17y + 4z = 80
175-80 = 25y + 75z -17y -4z
95 = 8y + 71z
8y + 71z = 95 •••••••••••(**)
So we have to solve x and xx simultaneously;
110y + 344z = 674
8y + 71z = 95
110/8 = 13.75 , so multiply equation xx by 13.75 and equation x by 1
110y + 344z = 674
110y + 976.25z = 1306.25
Subtract equation xx from x
(976.25z - 344z) = (1306.25 -674)
632.25z = 632.25
z = 632.25/632.25
z = 1
