B = no. of buses
v = no. of vans
b + v less than or equal to 8 ( there are only 8 drivers, but don't have to use them all)
51b + 8v greater than or equal to 193 (the number of seats must be at least 193 but there can be spares)
So these are the inequalities to solve. I did start doing a linear programming graph but the second inequality is horrible so I hope you don't need to actually solve them.
55.50 divided by 2 = 27.75
Only ask about the cost of tickets.
What we know:
line P endpoints (4,1) and (2,-5) (made up a line name for the this line)
perpendicular lines' slope are opposite in sign and reciprocals of each other
slope=m=(y2-y1)/(x2-x1)
slope intercept for is y=mx+b
What we need to find:
line Q (made this name up for this line) , a perpendicular bisector of the line p with given endpoints of (4,1) and (2,-5)
find slope of line P using (4,1) and (2,-5)
m=(-5-1)/(2-4)=-6/-2=3
Line P has a slope of 3 that means Line Q has a slope of -1/3.
Now, since we are looking for a perpendicular bisector, I need to find the midpoint of line P to use to create line Q. I will use the midpoint formula using line P's endpoints (4,1) and (2,-5).
midpoint formula: [(x1+x2)/2, (y1+y2)/2)]
midpoint=[(4+2)/2, (1+-5)/2]
=[6/2, -4/2]
=(3, -2)
y=mx=b when m=-1/3 slope of line Q and using point (3,-2) the midpoint of line P where line Q will be a perpendicular bisector
(-2)=-1/3(3)+b substitution
-2=-1+b simplified
-2+1=-1+1+b additive inverse
-1=b
Finally, we will use m=-1/3 slope of line Q and y-intercept=b=-1 of line Q
y=-1/3x-1
They can buy 33 pairs of skates. The remainder represents the part pf the skate they can almost buy with that money.
