5.5k views
1 vote
A local gym offers two choices in group discounts. Package A has a one-time enrollment fee of $205.59 per person and a monthly fee of $39.63. There is also an optional $15.48 monthly fee for full access to the swimming pool. Package B has a one-time enrollment fee of $185.64 per person and a monthly fee of $59.25. There is also an optional $22.38 monthly fee for full access to the swimming pool. Which package is best for a couple who wants to join the gym and utilize the pool for five years?

2 Answers

3 votes
A couple who want to join the gym and utilize the pool for five years, would have to pay one-time enrollment fee for two persons, monthly fee of gym and pool for 60 months.

Therefore Total Expenditure = (2 * one-time enrollment fee) + (2 * 60 * monthly fee of gym) + (2 * 60 * monthly fee of pool)

Now, Package A has a one-time enrollment fee of $205.59 per person and a monthly fee of $39.63. There is also an optional $15.48 monthly fee for full access to the swimming pool.

So Expenditure A = (2*205.59)+(2*60*39.63)+(2*60*15.48) = $7024.38

And, Package B has a one-time enrollment fee of $185.64 per person and a monthly fee of $59.25. There is also an optional $22.38 monthly fee for full access to the swimming pool.

So Expenditure B = (2*185.64)+(2*60*59.25)+(2*60*22.38) = $10,166.88

It is clearly visible that Expenditure B is more than Expenditure A. Hence, Package A is best option for the couple.
User Joseandro Luiz
by
8.3k points
1 vote

Step 1: Assign variable for the unknown

Let us try to identify the cost involved in each package. Let x be the number of people and y be the number of months.

Step 2: Identify expression for the given information

We need to write an expression to denote the total cost involved to join the gym and utilize the swimming pool for ' x ' number of people for 'y' number of months.

Statement 1: Package A has a one-time enrollment fee of $205.59 per person and a monthly fee of $39.63. There is also an optional $15.48 monthly fee for full access to the swimming pool.

So based on the statement 1

Cost for Package A = [205.59 + (39.63+15.48)y]x

Statement 2: Package B has a one-time enrollment fee of $185.64 per person and a monthly fee of $59.25. There is also an optional $22.38 monthly fee for full access to the swimming pool.

So based on the statement 2

Cost for Package B = [185.64 + (59.25+22.38)y]x

Step 3: Simplifying each expression

Package A = [205.59 + (39.63+15.48)y]x =[205.59+55.11y]x

Package B = [185.64 + (59.25+22.38)y]x = [185.64+81.63y]x

Step 4: Evaluate each expression

For a couple, Number of people (x) = 2, and for 5 years, Number of months (y) = 5 years × (12 month/year) = 60

We need to substitute 2 for x and 60 for y in the expression and see which package cost is lower to give the correct recommendation.

Package A: [205.59+55.11y]x = [205.59+55.11(60)]×2=$7024.38

Package B: [185.64+81.63y]x = [185.64+81.63(60)]×2=$10166.88

Conclusion:

Package A is cheaper than Package B. So we can conclude Package A is best for a couple who wants to join the gym and utilize the pool for five year.

User Fulrus
by
8.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories