Question

Camila has a points card for a movie theater.

Answer 1

Answer:  8 visits

========================================================

Explanation:

x = number of visits (some positive whole number)

2.5x = number of points earned for those x visits, ignoring bonus

2.5x+85 = number of points when adding on the 85 sign up bonus

We want that expression to be at least 105, which means we want it 105 or larger.

$2.5x+85 \ge 105\\\\2.5x \ge 105-85\\\\2.5x \ge 20\\\\x \ge 20\div 2.5\\\\x \ge 8$

So if x = 8 or larger, then she'll have 105 or more points.

Let's see if we get 105 when plugging in x = 8

2.5x+85 = 2.5*8+85 = 20+85 = 105

so that works out

Let's try something like x = 10

2.5x+85 = 2.5*10+85 = 25+85 = 110

I'll let you try other values of x.

----------

In short, she earns her first free movie ticket on the 8th visit.