Michael has a points card for a movie theater. He receives 70 rewards points just for signing up. He earns 8.5 points for each visit to the movie theater. He needs at least 165 points for a free movie ticket. What is the least number of visits he needs to make in order to earn a free movie ticket?

Answer

The true least number of visits is the lowest whole number above 11.176470..., which is 12.

Step-by-step explanation:

points per visit, # of visits + sign-up points ≥ free tickets points

8.5 (points per visit)  

70 (# of visits)

165 (free ticket points)

8.5v ≥ 70 + 165

70 + 8.5v ≥ 165

8.5v ≥ 165 -70

8.5v/8.5v ≥ 95/8.5

v ≥ 11.1764705882

The true least number of visits is the lowest whole number above 11.176470..., which is 12.

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2