For how many movies is the cost of the plans the same?

For 36 movies the cost of both the plans is same.

Step-by-step explanation:

Let us assume foe m movies, both the plans cost same.

Now, PLAN A:

Annual Fee = $45

Cost per movie  =  $2.50

⇒The cost of watching m movies  = m x (Cost of 1 movie)

= m x ($2.50) = 2.5  m

So, the total cost of Plan  A  = Annual Fee + Cost of m moves

                                                 = 45 + 2.50 m

PLAN B:

Cost per movie  =  $3.75

⇒The cost of watching m movies  = m x (Cost of 1 movie)

= m x ($3.75) = 3.75  m

ACCORDING TO QUESTION:

for m movies,  Cost of plan A = Cost of plan B

⇒45 + 2.50 m  = 3.75  m

or, 3.75 m  - 2.5 m = 45

or, m  = 45/1.25 = 36

or, m  = 36

Hence, for 36 movies the  cost of  both the plans is same.