Answer:
D
Step-by-step explanation:
The factor theorem states if (x - h) is a factor of a polynomial p(x) then
p(h) = 0
However, p(h) ≠ 0 then the value obtained is the remainder.
Thus
p(3) = - 2
When p(x) is divided by (x - 3) then the remainder is - 2
The cost of an adult ticket is $15.50 and the cost of a child ticket is $8.50
Proof:
Set up a system of equations calling Adults a and Children c
2a+3c= $56.50 (equation 1)
4c+a= $49.50 (equation 2)
a= -4c+49.50 (i subtracted 4c to both sides) (label equation 3)
sub equation 3 into equation 1
2(-4c+49.50)+3c= 56.50
-8c+99+3c=56.50
-5c+99=56.50
-99 -99
-5c = -42.50
c= -42.50/ -5
c= 8.50
sub c=8.50 into equation 3 to find adult price
a= -4(8.5)+49.50
a= 15.50
Therefore Child Cost = $8.50 and Adult Cost= $15.50