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Worksheet Grade 9 Social Studies & Civics

Setting Bridgeton's Water Rates: Tiered Pricing and Affordability

Grade 9 worksheet where students build a two-variable equation for a fictional town's tiered water rate, then test the bill against a real affordability threshold.

Objectives

  1. Students will write and solve a two-variable equation representing a tiered water rate.
  2. Students will calculate a household's water bill as a percentage of income and compare it to a real affordability threshold.
  3. Students will evaluate who benefits and who bears the greatest cost under a tiered pricing structure.

Vocabulary

Fixed charge
The part of a water bill that stays the same every month no matter how much water a family uses. It helps pay for the pipes, meters, and workers the utility needs even when no water is flowing.

Also: tiered rate, affordability threshold, capital improvement

Teacher overview

The fictional town of Bridgeton owns aging water pipes that need to be replaced, and its water board has proposed a new tiered rate to raise the money without asking every household to pay the same increase. This worksheet has students build the algebra behind that proposal, a fixed monthly fee plus a per-gallon charge that rises once a household crosses a set usage line, and then check the new bill against a widely used affordability threshold, a rule of thumb built from two EPA benchmarks. A common misconception in this worksheet is that a "tiered" rate charges every gallon at the higher rate once a household crosses the threshold; in fact, only the gallons above the threshold cost more, which is the same structure as a graduated income tax bracket. Students who assume the higher rate applies to the whole bill will overstate the bill in items 4 and 5, so watch for that error while checking work.

Setting Bridgeton's Water Rates: Tiered Pricing and Affordability — Grade 9 Social Studies & Civics
Name: ____________________________ Date: ______________

Student Worksheet

The fictional town of Bridgeton's water board is considering the following tiered rate to help pay for pipe replacement. Use these facts for every item below.

  • Fixed monthly charge: $18, regardless of usage.
  • Tier 1 rate: $0.006 per gallon for the first 6,000 gallons used in a month.
  • Tier 2 rate: $0.010 per gallon for every gallon used above 6,000 in that month.
  • Nationally, combined water and sewer bills rose about 24 percent from 2019 to 2024. A widely used rule of thumb treats a combined water and sewer bill above roughly 4.5 percent of household income as a high cost burden. That number comes from adding two EPA benchmarks, 2.5 percent for drinking water and 2 percent for wastewater; EPA itself has no single official cutoff.
  1. Write an equation for a household's monthly bill, C, when its usage, u, is 6,000 gallons or less. Use the fixed charge and the Tier 1 rate.
  2. Write a separate equation for a household's monthly bill, C, when its usage, u, is more than 6,000 gallons. Remember that only the gallons above 6,000 are charged at the Tier 2 rate.
  3. The Alvarez household uses 4,000 gallons in a month. Calculate their bill using your equation from item 1.
  4. The Okafor household uses 9,000 gallons in a month. Calculate their bill using your equation from item 2.
  5. Show your work for item 4 a second time using a different method (for example, calculating the two tiers separately and adding them, if you calculated it as one expression the first time). Confirm both methods give the same bill.
  6. The Ruiz household earns $2,400 per month and uses 9,000 gallons. Calculate their monthly water bill and express it as a percentage of their monthly income, rounded to the nearest tenth of a percent.
  7. Does the Ruiz household's bill fall above or below the 4.5 percent affordability threshold? By how many percentage points?
  8. The Delgado household earns $6,800 per month and also uses 9,000 gallons. Calculate their bill as a percentage of income and compare it to the Ruiz household's percentage.
  9. In two to three sentences, explain why a tiered rate can raise the same total revenue for pipe replacement while placing very different burdens on two households that use the same amount of water.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: C = 18 + 0.006u.
    The fixed charge of $18 plus the Tier 1 rate of $0.006 applied to every gallon, since usage stays at or below 6,000 gallons.
  2. Answer: C = 18 + 36 + 0.010(u - 6,000).
    The first 6,000 gallons are still billed at the Tier 1 rate (6,000 x 0.006 = $36), then every gallon above 6,000 is billed at the Tier 2 rate of $0.010, added to the $18 fixed charge.
  3. Answer: $42.
    C = 18 + 0.006(4,000) = 18 + 24 = $42.
  4. Answer: $84.
    C = 18 + 36 + 0.010(9,000 - 6,000) = 18 + 36 + 0.010(3,000) = 18 + 36 + 30 = $84.
  5. Answer: $84 (confirmed by a second method).
    Method two: bill the two tiers separately. Tier 1 portion: 6,000 gal x $0.006 = $36. Tier 2 portion: 3,000 gal x $0.010 = $30. Add the fixed charge: 18 + 36 + 30 = $84, matching item 4.
  6. Answer: 3.5 percent.
    The Ruiz bill is $84 (same usage as item 4). 84 / 2,400 = 0.035, which is 3.5 percent of monthly income.
  7. Answer: Below, by about 1.0 percentage point.
    3.5 percent is below the 4.5 percent threshold, a difference of 4.5 - 3.5 = 1.0 percentage point. This is the water bill alone, while the 4.5 percent threshold covers water and sewer combined, so adding a sewer bill would bring the Ruiz household closer to the threshold or above it.
  8. Answer: 1.2 percent, well below the Ruiz household's 3.5 percent.
    84 / 6,800 = 0.0124, which rounds to 1.2 percent. The Delgado household pays the same dollar amount but a much smaller share of its income, because the household earns nearly three times as much.
  9. Answer: Because the bill is a fixed dollar amount based on gallons used, not on income, the same $84 bill takes a far larger share of a lower income than a higher one, so the tiered structure raises the needed revenue while its true burden still depends heavily on the household's income, not only its water use.

Differentiation

Support (below grade level)

Provide the two equations from items 1 and 2 already written, with blanks only for the numeric coefficients, so students focus on substituting Ruiz and Okafor's usage rather than constructing the equations from scratch. Allow a calculator for every division step, and provide a worked percentage example (a different household, different numbers) before item 6.

Extension (above grade level)

Ask students to find the exact usage level, in gallons, at which the Ruiz household's bill would reach precisely 4.5 percent of its $2,400 monthly income, then to write and solve the equation that finds that usage level algebraically rather than by guess-and-check.

ELL supports

Pre-teach "tiered," "fixed charge," and "affordability threshold" with a simple diagram showing a bill split into two stacked bars, a wider bottom bar for Tier 1 and a narrower top bar for Tier 2 usage. Allow item 9 to be answered as two or three short sentences using a provided sentence frame: "The bill is the same dollar amount for both households, but it is a ___ percentage of income for ___ because ___."

The town, its households, and its rate figures in this scenario are fictional, chosen for classroom practice.