Option A $5.75 for each visit

Option B Yearly membership for $99, plus
$.50 for each visit

write an inequality that can be used to determine the minimum number of times a person would need to visit the gym in a year in order for option B to be less expensive than option A.

$5.75x > $99 + $.50 ??

$5.75v > $99 + $.50v

To determine the minimum number of times a person would need to visit the gym in a year for option B to be less expensive than option A, we can set up an inequality.

Let's assign the number of visits in a year as "x".

Option A costs $5.75 for each visit. So, the total cost of option A would be 5.75x.

Option B has a yearly membership fee of $99 and an additional charge of $0.50 for each visit. Therefore, the total cost of option B would be 99 + 0.50x.

To find the minimum number of visits required for option B to be less expensive than option A, we can set up the inequality:

5.75x > 99 + 0.50x

Now, we can simplify the inequality:

5.75x - 0.50x > 99

5.25x > 99

Dividing both sides of the inequality by 5.25:

x > 99 / 5.25

The minimum number of visits needed for option B to be less expensive than option A is approximately 18.86. However, since we cannot have a fractional number of visits, the minimum number of visits would be 19.