Sarah and Joe are seeking to join a gym. Sarah saw on television that Great Gym is offering membership at $19.50 per month, plus a one-time registration fee of $59. Joe plans to join Wacky Workout World because Wacky Workout World only charges $9.50 per month, plus a one-time registration fee of $149.
Write an expression to represent the membership cost of Wacky Workout World for x months.
3.If Sarah decides to join Great Gym and Joe joins Wacky Workout World, who would pay less during the first month of membership? Show your work.
4.If Sarah decides to join Great Gym and Joe joins Wacky Workout World, who would pay less during the first year of membership? Show your work.
5. Both gym memberships will eventually have a month in which the cost to attend either gym would be the same. How long would this membership be and how much would it cost? Show your work.
6. Which gym membership is a better deal? Explain why.
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3. The expression to represent the membership cost of Wacky Workout World for x months would be:
Cost = (9.50 * x) + 149
4. To find out who would pay less during the first year of membership, we need to compare the total cost for both gyms.
For Great Gym:
Monthly cost = $19.50 + $59 (one-time registration fee)
Annual cost = 12 * ($19.50 + $59) = $888
For Wacky Workout World:
Monthly cost = $9.50 + $149 (one-time registration fee)
Annual cost = 12 * ($9.50 + $149) = $1944
Therefore, Sarah would pay less during the first year of membership by choosing Great Gym.
5. To find the month at which the cost to attend either gym would be the same, we need to set the two expressions equal to each other and solve for x.
(9.50 * x) + 149 = (19.50 * x) + 59
9.50x + 149 = 19.50x + 59
10x = 90
x = 9
So, the cost to attend either gym would be the same after 9 months, and it would cost $9.50 * 9 + $149 = $225.50.
6. In this case, Great Gym is the better deal because it has a lower monthly cost and a lower one-time registration fee. Over time, even though Joe pays less per month at Wacky Workout World, the higher registration fee offsets the savings. Therefore, Sarah would pay less during the first month, the first year, and in the long run by choosing Great Gym.
I'd be happy to help you with these questions! Let's break it down one by one:
3. To calculate the membership cost of Wacky Workout World for x months, we need to multiply the monthly cost by the number of months and add the one-time registration fee. The expression would be:
Membership cost of Wacky Workout World = (9.50 * x) + 149
4. To find out who would pay less during the first year of membership, we need to calculate the total cost for each gym for 12 months (assuming a year).
For Great Gym:
Total cost for Great Gym = (19.50 * 12) + 59
For Wacky Workout World:
Total cost for Wacky Workout World = (9.50 * 12) + 149
You can compare the two total costs to determine who would pay less.
5. To find the month in which the cost to attend either gym would be the same, we can set up an equation where the total costs of each gym are equal:
(19.50 * x) + 59 = (9.50 * x) + 149
Simplifying the equation, we can solve for x:
10x + 59 = 9.50x + 149
0.50x = 90
x = 180
So, after 180 months (or 15 years), the membership cost for both gyms would be the same. The cost would be:
Cost after 180 months = (19.50 * 180) + 59 = $3789
6. To determine which gym membership is a better deal, you can compare the total costs.
If you compare the total costs for different time periods, like the first month or the first year, you'll have a clearer idea of which gym is more cost-effective.
In this case, you can compare the total cost during the first month and the first year for both gyms:
For Great Gym:
Total cost during the first month = 19.50 + 59
Total cost during the first year = (19.50 * 12) + 59
For Wacky Workout World:
Total cost during the first month = 9.50 + 149
Total cost during the first year = (9.50 * 12) + 149
Compare the totals, and you'll find out which gym membership is a better deal based on your preferred time frame.
I hope this helps! Let me know if you have any further questions.