You are a transit systems engineer at GreenLine, the city's new electric bus network. Use ratio tables, graphs, and unit rates to size the fleet, plot the ridership line, pick the best vendor, and mix the official route color — so the whole system runs on one steady ratio.
GreenLine's pilot route moved 240 riders using 3 buses. Every part of your design must keep that same ratio of riders to buses so service stays even and on time.
CORE RATIO 3 buses : 240 riders · that is 80 riders per bus (the unit rate)
A ratio compares two amounts, like 3 buses to 240 riders. Equivalent ratios are the same comparison scaled up or down (×2, ×3, …). A unit rate is the amount for just one (riders for 1 bus = 240 ÷ 3 = 80).
Español: Una razón compara dos cantidades, como 3 autobuses a 240 pasajeros. Las razones equivalentes son la misma comparación escalada (×2, ×3, …). Una tasa unitaria es la cantidad para uno solo (240 ÷ 3 = 80 pasajeros por autobús).Fill in the missing riders for each bus count. Every column must keep the same ratio: 80 riders per bus. The shaded "Pilot data" column (3 buses, 240 riders) is given — use it to scale each new column. Then answer Q1.4 to find the unit rate.
| Quantity | Pilot data | Q1.1 | Q1.2 | Q1.3 |
|---|---|---|---|---|
| Buses | 3 | 5 | 9 | 12 |
| Riders | 240 |
Tip: each bus carries the same 80 riders. Multiply the bus count by 80, or scale the whole 3 : 240 column.
Q1.4 — Unit rate: how many riders does 1 bus carry? (Hint: 240 ÷ 3)
To find the unit rate, divide riders by buses: 240 ÷ 3. To fill a column, multiply the number of buses by that unit rate.
Español: Para la tasa unitaria, divide pasajeros entre autobuses: 240 ÷ 3. Para llenar una columna, multiplica los autobuses por esa tasa.Write an equation that gives riders y for any number of buses x. Use your unit rate. (You will graph this line in Task 2.)
Every (buses, riders) pair from your ratio table lands on one straight line through the origin. The graph below plots that line with three labeled points. Drag the blue point along the line, then use the dashed guide lines to read off values for Q2.1 and Q2.2.
At 7 buses the line reads 560 riders (7 × 80).
Q2.1 — Follow the dashed lines to the blue point at x = 7 buses. How many riders is that?
Q2.2 — Demand jumps to 800 riders. Reading the line, how many buses does GreenLine need?
To read a graph: go up from the bus number until you hit the line, then go left to the riders axis. Each step right is 1 bus; each step up is 80 riders.
Español: Para leer la gráfica: sube desde el número de autobuses hasta la línea, luego ve a la izquierda hasta el eje de pasajeros. Cada paso a la derecha = 1 autobús; cada paso arriba = 80 pasajeros.Why does this line have to pass through (0, 0)? Explain using the idea that 0 buses can carry 0 riders, and why that makes the graph a proportional relationship.
Two vendors bid to supply fast chargers. They quote different bundles, so compare the unit cost (price for one charger) to find the better deal. Tap the vendor you would choose.
Find each unit cost first, then choose. The card you pick is checked when you submit.
Q3.1 — VoltEdge unit cost ($7,200 ÷ 6 chargers)
Q3.2 — AmpWorks unit cost ($9,200 ÷ 8 chargers)
Unit cost = total price ÷ number of items. The cheaper unit cost is the better deal, even if the total price is bigger.
Español: Costo unitario = precio total ÷ número de artículos. El menor costo unitario es la mejor oferta, aunque el precio total sea mayor.GreenLine needs 24 chargers. How much would the whole order cost from the cheaper vendor, and how much do you save versus the other vendor for 24 chargers?
Every GreenLine sign uses the same official color: a paint mixed in the ratio 3 parts teal to 2 parts white. Build one batch, watch the swatch update, then scale it up so the mix stays identical.
The swatch only matches the official GreenLine color when your mix is equivalent to 3 : 2 (like 6 : 4 or 9 : 6).
Q4.1 — A big job uses 15 parts teal. To keep the 3 : 2 ratio, how many parts white?
Q4.2 — How many total parts of paint is that full batch (teal + white)?
Scaling a mix: multiply both parts by the same number. If teal goes from 3 to 15 (×5), white must also go ×5: 2 × 5 = 10.
Español: Para escalar una mezcla, multiplica las dos partes por el mismo número. Si el verde azulado va de 3 a 15 (×5), el blanco también: 2 × 5 = 10.What fraction of the whole batch is teal? Write it as a fraction and as a percent, and explain why that percent never changes no matter how big the batch is.
When the table, graph, vendor pick, and color mix all check out, submit your network plan to the city. Enter your name in the field below, then press Submit plan & grade to save your score as a PDF or DOC.
| Level | Score | Descriptor |
|---|---|---|
| 4 — Exceeds | 10 / 10 | Builds the ratio table from equivalent ratios, reads the ridership graph both directions, computes both vendor unit costs and picks the cheaper option, and scales the paint mix correctly. Can explain why all table pairs fall on one line through the origin. |
| 3 — Meets | 8–9 / 10 | Completes the table and unit rate, reads the graph accurately, and picks the cheaper vendor with at most one arithmetic slip. Scales the mix correctly. |
| 2 — Approaching | 5–7 / 10 | Finds simple equivalent ratios but struggles to read the graph or to compare by unit cost (e.g., compares totals instead of unit rates). Partial scaling or table. |
| 1 — Beginning | 0–4 / 10 | Few correct values. Confuses the parts of a ratio or does not keep the ratio constant when scaling. Needs reteaching on unit rate and equivalent ratios. |