Water for Schools
Menu

Worksheet Grade 7 Math

Blue Harbor Water Bill: A Multistep Percent Increase Worksheet

A grade 7 math worksheet where students compute two households' water bills before and after a rate increase, applying multistep percent reasoning to a fictional utility.

Objectives

  1. Students will compute a household's total monthly water bill from a fixed fee, a volumetric rate, and a flat fee.
  2. Students will apply a percent increase to individual bill components and to a household's total bill.
  3. Students will compare percent increases between two households and explain why they differ.

Vocabulary

Volumetric rate
The price a customer pays for each unit of water actually used. Using more water makes this part of the bill bigger, so it rewards saving water.

Also: fixed fee, percent increase

Teacher overview

This worksheet uses the fictional town of Blue Harbor to give students practice with the kind of multistep percent problem that appears on a real water bill. Blue Harbor's water utility charges three separate parts on every bill: a fixed monthly fee, a volumetric rate based on gallons used, and a flat stormwater fee, and the utility board has approved a percent increase to two of those three parts. Students calculate two households' bills under the old and new rates and discover that the overall percent increase in a total bill is not the same as any single component's percent increase, because the fixed fee does not change.

Blue Harbor Water Bill: A Multistep Percent Increase Worksheet — Grade 7 Math
Name: ____________________________ Date: ______________

Student Worksheet

The fictional town of Blue Harbor bills water customers using three parts each month:

  • A fixed fee of $15.00, charged to every customer no matter how much water they use.
  • A volumetric rate of $6.00 for every 1,000 gallons used.
  • A stormwater fee of $3.00, a flat monthly charge.

The utility board has approved these changes, effective next month:

  • The fixed fee does not change.
  • The volumetric rate increases by 12%.
  • The stormwater fee increases by 20%.

The Ortiz family uses 6,000 gallons per month. The Chen family uses 10,000 gallons per month.

  1. Calculate the Ortiz family's old total monthly bill. Add the fixed fee, the volumetric charge, and the stormwater fee.
  2. Calculate the utility's new volumetric rate after the 12% increase.
  3. Calculate the new stormwater fee after the 20% increase.
  4. Calculate the Ortiz family's new total monthly bill. Use the unchanged fixed fee and your answers from items 2 and 3.
  5. Calculate the dollar increase in the Ortiz family's total monthly bill. Subtract the old bill from the new bill.
  6. Calculate the percent increase in the Ortiz family's total monthly bill. Round to the nearest tenth of a percent. (Percent increase = increase ÷ old bill × 100.)
  7. Explain why the percent increase in item 6 is smaller than the 20% increase applied to the stormwater fee alone.
  8. Calculate the Chen family's old total monthly bill using the current rates.
  9. Calculate the Chen family's new total monthly bill using the new rates. Then calculate their percent increase, rounded to the nearest tenth of a percent.
  10. Which family had the larger percent increase in their total bill, the Ortiz family or the Chen family? Compare each family's fixed fee to their total bill to explain why.
  11. A new customer, the Alvarez family, has an old bill of $54.00. This matches the Ortiz family's old bill. Suppose the Alvarez family's water use also matches the Ortiz family's. Will their percent increase also equal the Ortiz family's answer from item 6? Explain your reasoning.

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: $54.00. Fixed fee $15.00, plus volumetric charge (6,000 gal ÷ 1,000 = 6 units × $6.00 = $36.00), plus stormwater fee $3.00: 15.00 + 36.00 + 3.00 = $54.00.
  2. Answer: $6.72 per 1,000 gallons. $6.00 × 1.12 = $6.72.
  3. Answer: $3.60. $3.00 × 1.20 = $3.60.
  4. Answer: $58.92. Fixed fee $15.00 (unchanged), plus volumetric charge (6 units × $6.72 = $40.32), plus stormwater fee $3.60: 15.00 + 40.32 + 3.60 = $58.92.
  5. Answer: $4.92. 58.92 − 54.00 = $4.92.
  6. Answer: 9.1%. 4.92 ÷ 54.00 ≈ 0.0911, which is about 9.1%.
  7. Answer: The 20% increase applies only to the $3.00 stormwater fee, a small part of the total bill, and the fixed fee does not increase at all. Because the total bill blends a part that did not change (the fixed fee) with parts that changed by 12% and 20%, the overall percent increase ends up smaller than either individual rate increase.
  8. Answer: $78.00. Fixed fee $15.00, plus volumetric charge (10,000 gal ÷ 1,000 = 10 units × $6.00 = $60.00), plus stormwater fee $3.00: 15.00 + 60.00 + 3.00 = $78.00.
  9. Answer: $85.80 (a 10.0% increase over the old bill). New bill: 15.00 + (10 × $6.72 = $67.20) + $3.60 = $85.80. Increase: 85.80 − 78.00 = $7.80. Percent increase: 7.80 ÷ 78.00 = 0.10, or 10.0%.
  10. Answer: The Chen family, with a 10.0% increase versus the Ortiz family's 9.1% increase. The Chen family's $15.00 fixed fee makes up a smaller share of their $78.00 old bill (about 19%) than the Ortiz family's $15.00 fixed fee makes up of their $54.00 old bill (about 28%). Because a smaller share of the Chen bill is "protected" from the increase by the unchanged fixed fee, a larger share of their bill rises by the full rate increases, pushing their overall percent increase closer to the underlying 12% and 20% changes.
  11. Answer: 9.1% (yes, the same as item 6). If two households have identical water use, every part of their bill (fixed fee, volumetric charge, and stormwater fee) is calculated the same way, so their old bills, new bills, and percent increases will all be identical.

Differentiation

Support (below grade level)

Provide a pre-filled table with rows for "Fixed fee," "Volumetric charge," and "Stormwater fee," and columns for "Old amount" and "New amount," so students fill in each cell before adding the column totals for items 1 and 4. Allow a calculator for every computation item.

Extension (above grade level)

Ask students to find how many gallons a family would need to use per month for their fixed fee to make up exactly 10% of their old total bill, then explain whether that family's percent increase would be closer to the Ortiz family's or the Chen family's.

ELL supports

Pre-teach fixed fee, volumetric rate, and percent increase using a simple bill diagram with three labeled boxes. Provide the percent increase formula as a written template students can fill in directly: "increase () ÷ old bill () = ___, which is ___%."

Extensions

Have students research their own family's water bill, if available, and identify whether it uses a fixed fee, a volumetric rate, or both, then compare its structure with Blue Harbor's three-part bill.