Question

Darrell and Jim are planning to run in their office-sponsored marathon and plan on joining a gym to train.Darrell finds that gym-A has a $40 joining fee and then costs $15 per month after that.Jim finds that gym-B is free to join and costs $20 per month after. At what number of months of training would gym-A to be a cheaper option than gym-B

Answer 1

Gym-A becomes the cheaper option after more than 8 months of training, based on the monthly and joining fees of both gyms.

Step-by-step explanation:

To determine at what number of months of training gym-A becomes a cheaper option than gym-B, we need to set up an equation to compare the total costs of both gyms over time. The total cost for gym-A can be represented by the equation C_A = 40 + 15m, where C_A is the total cost of gym-A and m is the number of months. Similarly, the total cost for gym-B is C_B = 20m.

To find when gym-A is cheaper than gym-B, we look for the value of m where C_A < C_B:

1. Set up the inequality: 40 + 15m < 20m.
2. Subtract 15m from both sides to get: 40 < 5m.
3. Divide both sides by 5 to solve for m: m > 8.

Therefore, gym-A becomes the cheaper option after more than 8 months of training.

Answer 2

From number of month to be 9, training would be cheaper in gym A than in gym B.

Step-by-step explanation:

To calculate the number of months when option containing gym A becomes cheaper than option of gym B, we first need to form cost equations for both and equate them.

Let x be the number of months.

The cost of gym A is = 40 + 15x

The cost of gym B = 20x

40 + 15x = 20x

40 = 20x - 15x

40 = 5x

x = 40/5

x = 8

So, the cost for both options will be equal when the number of months is 8. From number of month to be 9, training would be cheaper in gym A than in gym B.