Super Yoga plans: Solving systems by substitution | Linear equations | Algebra I | Khan Academy

TL;DR

The cost of gym membership plans depends on the number of sessions attended, with the trial plan being cheaper for less than 5 sessions and the basic plan being cheaper for more than 5 sessions.

Transcript

In the last video we began to visually explore the relationship between the number of sessions I attend and my monthly cost given the different plans. So right here, in this blue line we visualized it for the trial plan, and then this orange dotted line we visualized it for the basic plan. And it meets where it intuitively, hopefully represents wha... Read More

Key Insights

• 🌱 The trial plan is cheaper than the basic plan for fewer than 5 sessions.
• 🌱 The basic plan becomes cheaper than the trial plan for more than 5 sessions.
• 😥 At the intersection point of 5 sessions, both plans have the same cost.
• 🌱 The cost per session is lower under the trial plan compared to the basic plan.
• 🌱 Adding more sessions increases the cost of the trial plan more rapidly than the basic plan.
• 🌱 The decision of which plan to choose depends on the expected number of sessions per month.
• 🌱 Choosing the trial plan is cost-effective for less than 5 sessions per month.

Questions & Answers

Q: What is the significance of the intersection point?

The intersection point represents the number of sessions where both the trial and basic plan have the same cost. It is a crucial point in deciding which plan is cheaper.

Q: How much does one session cost under each plan?

Under the trial plan, one session costs $12, while under the basic plan, one session costs $28.

Q: How can we find the exact value of the intersection point?

By setting up an equation, we can determine the number of sessions (s) that makes the cost of each plan equal. The equation is 12s = 20 + 8s, and solving it gives s = 5.

Q: Is it necessary to calculate the cost under the basic plan for 5 sessions?

No, because the intersection point was found at 5 sessions, which means the cost is already known to be $60 for both plans.

Summary & Key Takeaways

• The trial plan has no upfront cost and adds $12 to the monthly cost for each session attended.

• The basic plan has an upfront cost of $20 and adds $8 to the monthly cost for each session attended.

• The intersection point occurs at 5 sessions, where both plans have the same cost of $60.