Question

You are comparing gym membership plans. Plan A requires you to pay $50 to join, and then $15 every month. Plan B is $30 to join, but $20 a month. What is the minimum number of months you would need to be a member for Plan A to be the cheaper option?

Answer 1

To find when Plan A becomes cheaper than Plan B, set up an inequality based on their costs, solve for the number of months, and round up to the next full month. It's calculated that after 5 full months of membership, Plan A becomes the cheaper option.

Step-by-step explanation:

To determine the minimum number of months needed for Plan A to be the cheaper option compared to Plan B, we need to set up an inequality and solve for the number of months. Let's denote the number of months as m.

For Plan A, the total cost after m months is comprised of a $50 joining fee plus $15 for each month, which can be represented as Cost_A = 50 + 15m. For Plan B, the total cost is a $30 joining fee plus $20 per month, resulting in Cost_B = 30 + 20m.

To find out when Plan A becomes cheaper, we need Plan A's cost to be less than Plan B's cost, which gives us the inequality:
50 + 15m < 30 + 20m.

Subtracting 15m from both sides:
50 < 30 + 5m.

Now, subtract 30 from both sides to isolate the term with m:
20 < 5m.

Finally, divide by 5 to solve for m:
m > 4.

Since we can't have a fraction of a month in this context, we need at least 5 full months for Plan A to be the cheaper option.