how can I Identify the number of solutions without solving.

Question

Identify the number of solutions without solving.

Raheel is comparing the cost of two parking garages. Garage A charges a flat fee of $6 per car plus $0.50 per hour. Garage B charges a flat fee of $2 per car plus $1 per hour.

pick one solutions that could represent this :

----> exactly one solution

----> no solution

---> infinitely many solutions

Answer 1

A = 6 +.5h

B = 2+h

let h = any integer

such as 6 hours, then

A = 9, B = 8 and B is cheaper

for any h A or B will be cheaper

unless 6+h/2 = 2+h

and h = 8 hours, then they both cost the same = 10

for more than ten hours 'A is cheaper

less than ten, B is cheaper

exactly ten they cost the same