Two sneaker resale platforms charge fees differently. Same shoes — different math. Find out which saves money and when the winner changes.
The sneaker price is the because I choose how much to spend.
The platform fee is the because it changes based on the shoe price.
In y = kx, k = 0.09 is the — the fee goes up by 9 cents per dollar of shoe price.
x = because I choose how much to spend on sneakers.
y = because it changes based on the shoe price.
For Platform A, as x (price) goes up, y (fee) .
For Platform B, as x goes up, y because the fee is always of the price.
| Shoe Price — x | Platform A Fee ($) | Platform B Fee ($) |
|---|---|---|
| $50 | ||
| $100 | ||
| $150 | ||
| $200 | ||
| $250 |
Both platform fees are the same when sneakers cost about $. At that price, both charge $.
Platform is cheaper for $50 sneakers. It charges $ vs $, saving $.
k = 0.09 means for every $1 the sneakers cost, the fee goes up by $ (9 cents).
Platform A's fee is always $15, so Platform A is — fee doesn't change with x.
Use Platform B's equation to find the fee for $175 sneakers:
y = 0.09 × 175 = $. So $175 sneakers cost $ in fees on Platform B.
What shape does Platform A's line make, and why?
Platform A makes a line because its cost
What shape does Platform B's line make, and what does that tell us?
Platform B makes a line that goes because each extra $ shoe price adds $
Do the lines cross? If yes, at approximately what $ shoe price amount?
Yes / No — the lines look like they cross near $ shoe price
What does the crossing point mean in this situation?
At that crossing point, both plans cost the same ($). Before it, is cheaper. After it, is cheaper.
For sneakers costing less than $, use Platform because its fee is lower.
For sneakers costing more than $, use Platform because its fee is lower.
My table shows: at $200 shoes, Platform A charges $ and Platform B charges $, so Platform saves $.
My graph shows Platform B's line is , which means as shoe price goes up, Platform B's fee grows .
x = ___ because ___ . y = ___ because it depends on the shoe price.
Platform B's equation is y = ___ x. The k value of ___ means that for every $1 of shoe price, the fee goes up by $___ .
For $120 sneakers: Platform A charges $___ . Platform B charges 0.09 × 120 = $___ . I recommend Platform ___ because it saves $___ .
Two sneaker resale platforms charge fees differently. Same shoes — different math. Find out which saves money and when the winner changes.
What is the independent variable? Write a complete explanation.
The independent variable is because I choose how much to spend on sneakers.
What is the dependent variable? Explain why it depends on x.
The dependent variable is because it changes based on the shoe price.
If x (price) goes up, y (fee) goes for Platform B because the fee is % of whatever x is.
| Shoe Price — x | Platform A ($) | Platform B ($) | Lower Fee |
|---|---|---|---|
| $50 | |||
| $100 | |||
| $167 | |||
| $200 | |||
| $300 | |||
Describe the pattern as shoe price rises. What happens to each platform's fee and why?
As shoe price increases, Platform A's fee because .
Platform B's fee because .
The Lower Fee column switches from Platform to Platform at around $.
What is Platform B's k value and what does it mean for sneaker buyers?
Platform B's k = . This means for every $1 the sneakers cost, the fee goes up by $ (9 cents).
So k is the — it tells me how quickly the fee grows as shoe price increases.
Is Platform B a proportional relationship? Use both the equation and table to explain.
Platform B is proportional because its equation is y = 0.09x — it's in form.
In my table, when x doubles from $100 to $200, y also from $ to $.
Use Platform B's equation to find the fee for $250 sneakers:
y = 0.09 × 250 = $. So $250 sneakers cost $ in fees on Platform B.
Give the approximate coordinate where the two lines cross:
The lines cross at approximately ( $ shoe price , $ )
What does that crossing point mean for someone choosing between Platform A and Platform B?
At that point, both options cost $. If you need fewer than $ shoe price, use because it's cheaper.
If you need more than $ shoe price, switch to because
Describe Platform A's line shape and explain it using the equation:
Platform A's line is because its equation is y = , which means the cost
never / always changes as x increases.
What does the steepness of Platform B's line tell you about its k value?
The steeper the line, the the k value. {plan_b}'s k = , so every unit of x adds $ to the cost.
My table shows the Lower Fee column switches from Platform to Platform at around $.
At $200 sneakers, Platform A charges $ and Platform B charges $, a difference of $.
Platform B's equation y = 0.09x shows k = $0.09 per dollar of shoe price, meaning every dollar adds $ to the fee.
Platform B is cheaper than Platform A ($15) when 0.09 × x is than $15, which happens when x is than $.
On my graph, the lines cross at about ( $, $ ).
To the left, Platform is cheaper. To the right, Platform is cheaper.
For sneakers costing less than $, use Platform . For sneakers over $, use Platform .
Platform A's fee is always $15 (no k × x). Platform B's k = 0.09. This tells me Platform B grows ___ expensive faster because ___ . For cheap sneakers, Platform ___ is better; for expensive ones, Platform ___ is better.
My graph's crossing point is at ( $___ , $___ ). To the left use Platform ___ . To the right use Platform ___ because at that price, 9% of the shoe price is ___ than $15.
For $150 sneakers: Platform A = $___ . Platform B = 0.09 × 150 = $___ . The cheaper platform is ___ , saving $___ .
Platform C: $10 membership + 5% per shoe. Equation: y = 0.05x + 10. What is Platform C's k value? Find the fee for $200 sneakers. Add Platform C to your graph.
Platform C's k = . At $200 sneakers: y = 0.05 × 200 + 10 = $ + $10 = $.
On my graph, Platform C starts at y = $ and rises than Platform B.
Three sneaker resale platforms. Compare all three — find which is cheapest and when the winner changes.
Before calculating: predict which platform is cheapest at $50 and at $300 sneakers. Use vocabulary terms.
At $50 I predict Platform is cheapest because its k / fee structure means .
At $300 I predict Platform wins because .
Do you think one platform is always cheapest, or does the winner change?
I think the winner because Platform A has a fee while Platform B has a k of .
Platform C's lower k (0.05 vs 0.09) means it might beat Platform B when .
| Shoe Price — x | Platform A ($) | Platform B ($) | Platform C ($) | Winner |
|---|---|---|---|---|
| $50 | ||||
| $100 | ||||
| $167 | ||||
| $200 | ||||
| $300 |
My prediction was because .
I was surprised that at $, Platform was cheaper than I expected because .
The Winner column changes times, creating different price zones.
Compare Platform B's k and Platform C's k. What does a smaller k value mean for buyers?
Platform B: k = per dollar. Platform C: k = per dollar.
Platform C has a k, which means its fee grows as shoe price increases.
A smaller k = lower rate of change, so for very expensive sneakers, Platform will be less expensive.
Which platforms are proportional? Which are not? Explain using the equation form.
Platform B is proportional because its equation is y = 0.09x — it's in y = kx form. If x = $0, y = $.
Platform C is proportional because of the + 10 — even at x = $0, you'd still pay $.
Platform A is proportional because y = 15 regardless of x.
Use Platform C's equation to find the fee for $200 sneakers:
y = 0.05 × 200 + 10 = $ + $10 = $. So $200 sneakers cost $ in fees on Platform C.
Platform C charges $17.50. What was the shoe price? Steps set up for you:
Start: 17.50 = 0.05x + 10. Subtract 10: = 0.05x. Divide by 0.05: x = $.
Where do Platform A and Platform B cross? What does that mean?
Platform A and Platform B cross at about ( $ shoe price , $ ).
At that point both cost exactly $. Before it is cheaper; after it is cheaper.
Where do Platform A and Platform C cross? What does that mean?
Platform A and Platform C cross at about ( $ shoe price , $ ).
This means at that point both cost exactly $. Before it is cheaper; after it is cheaper.
Describe the three zones your graph creates — which plan is cheapest in each?
Zone 1 (0 to $ shoe price): is cheapest because its line is the lowest here.
Zone 2 ( to $ shoe price): wins because
Zone 3 (above $ shoe price): is cheapest because
Why is the graph more useful than just the table for finding these zones?
The graph shows all three lines at once, so I can see the crossing points at a glance. With only the table, I would have to
The Winner column changes times, creating zones.
Platform wins for low-priced sneakers (under $) because .
Platform A: flat $15 (no k × x). Platform B: k = 0.09 (grows fastest). Platform C: k = 0.05 + $10 start.
Because Platform B's k is than Platform C's k, Platform B becomes more expensive .
Platform C's $10 fee means it starts higher, but eventually .
My graph has crossing points, creating zones.
Zone 1 ($0 to $): Platform is cheapest.
Zone 2 ($ to $): Platform wins.
Zone 3 (above $): Platform is cheapest because .
Sneakers under $ → use Platform .
Between $ and $ → use Platform .
Over $ → use Platform because .
Platform B's k = 0.09 and Platform C's k = 0.05. This means Platform ___ grows more expensive faster because ___ . For very expensive sneakers, Platform ___ is the best deal because ___ .
At $167 sneakers: Platform A = $___ . Platform B = 0.09 × 167 = $___ . Platform C = 0.05 × 167 + 10 = $___ . The cheapest platform at $167 is Platform ___ .
My graph has ___ zones. Zone 1 ($0 to $___ ): Platform ___ cheapest. Zone 2 ( $___ to $___ ): Platform ___ cheapest. Zone 3 (above $___ ): Platform ___ cheapest.