A trampoline park that you frequently go to is $9 per visit. You have the option to purchase a monthly membership for $30 and then pay $4 for each visit. Explain whether you will buy the membership, and why. Option A: y = $9x Option B: y = $30 + $4x

Answer 1

To determine whether purchasing the monthly membership is a better option than paying per visit, we can set up the equations based on your usage.

Option A: Pay per visit. The cost function is: $$y=9x$$ where $y$ is the total cost and $x$ is the number of visits.

Option B: Monthly membership. The cost function is: $$y=30+4x$$ where $y$ is the total cost and $x$ is the number of visits.

Now, we can compare the two cost functions to find the break-even point, which is when both costs are equal:

$$9x=30+4x$$

To solve for $x$:

1. Subtract $4x$ from both sides: $$9x-4x=30$$ $$5x=30$$

2. Divide by 5: $$x=6$$

This means that if you plan to visit the trampoline park more than 6 times in a month, the membership option will be cheaper.

• If you visit 6 times:

  • Option A: $9\times 6=54$
  • Option B: $30+4\times 6=30+24=54$ (break-even)

• If you visit 7 times:

  • Option A: $9\times 7=63$
  • Option B: $30+4\times 7=30+28=58$ ( membership is cheaper)

• If you visit 5 times:

  • Option A: $9\times 5=45$
  • Option B: $30+4\times 5=30+20=50$ (pay per visit is cheaper)

Given this analysis, it would make sense to buy the membership if you plan to visit more than 6 times in a month. If you anticipate using the trampoline park less than or equal to 6 times, then it would be more cost-effective to pay the regular fee of $9 per visit.