To evaluate whether to buy the membership or pay per visit, we have two options represented by the equations:
- Option A: Pay per visit: \( y = 9x \)
- Option B: Monthly membership: \( y = 30 + 4x \)
Break-even Point
We already found the break-even point by equating the two equations:
\[ 9x = 30 + 4x \] \[ 5x = 30 \] \[ x = 6 \]
This means that if you visit the trampoline park more than 6 times in a month, the membership ($30 + $4 per visit) becomes more economical than paying $9 for each visit.
Anya's Choice
Anya is traveling from out of town and will only visit the trampoline park once.
- For one visit (x = 1): \[ \text{Option A: } y = 9(1) = 9 \] \[ \text{Option B: } y = 30 + 4(1) = 30 + 4 = 34 \]
Since Anya will only visit once, she should choose Option A (pay per visit) for $9, as it is much cheaper than the membership cost of $34.
Jin's Choice
Jin plans on going to the trampoline park seven times this month.
- For seven visits (x = 7): \[ \text{Option A: } y = 9(7) = 63 \] \[ \text{Option B: } y = 30 + 4(7) = 30 + 28 = 58 \]
Here, Jin should choose Option B (monthly membership) since the total cost of $58 is cheaper than the $63 for paying per visit.
Point of Intersection Interpretation
The point of intersection of the two graphs represents the break-even point, which occurs at \( x = 6 \) visits. This point tells us that at 6 visits, both payment options cost the same amount of money ($54). It signifies the threshold where it becomes more economical to choose the membership instead of paying for each visit. For any number of visits above 6, the membership option is the more cost-effective choice.