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Math problem set Grade 7 Math

Blending Peckhaven's Two Wells: A Grade 7 PFAS Mixing Set

Students weight each well's PFOA level by its share of the blended flow, compare that result to a plain average, and find the percent drop needed to meet the limit.

Objectives

  1. Students will find each well's share of a blended flow as a fraction and a decimal.
  2. Students will compute a blended contaminant level weighted by flow.
  3. Students will calculate the percent decrease needed to reach a stated limit.

Vocabulary

PFOA
One of the oldest and most studied PFAS chemicals, once used to make nonstick coatings. It is no longer made in the United States, but it stays in water and soil for a very long time.
Parts per trillion
A unit for measuring extremely small amounts of a chemical in water. PFAS limits are set in parts per trillion because these chemicals matter even in tiny doses.

Also: blend, weighted average

Teacher overview

Peckhaven is a fictional town that draws its drinking water from two wells and mixes them in one pipe before the water reaches homes. Federal rules set the maximum contaminant level for PFOA at 4.0 parts per trillion, and water systems must meet it by April 2029. A May 2026 EPA proposal, not final as of September 2026, would let eligible systems apply for a two-year exemption without changing that limit, so a small system with one clean well and one contaminated well has a genuine decision to make about how much to pump from each. The misconception this set corrects is the habit of averaging the two well readings straight across. A plain average assumes the wells contribute equally, while the blend actually follows each well's share of the total flow, so the well pumping more water pulls the blended number toward its own reading.

Blending Peckhaven's Two Wells: A Grade 7 PFAS Mixing Set — Grade 7 Math
Name: ____________________________ Date: ______________

Problems

Peckhaven is a fictional town, and every flow and test result below was written for this problem set. Well A tests at 12 parts per trillion of PFOA and pumps 300 gallons per minute. Well B tests at 2 parts per trillion and pumps 700 gallons per minute. The two wells feed one pipe.

  1. How many gallons per minute reach the blending pipe in all?
  2. Use the 1,000 gallons per minute from problem 1. What fraction of the blended water comes from Well A? Write it as a decimal.
  3. What fraction of the blended water comes from Well B? Write it as a decimal.
  4. Multiply Well A's level of 12 parts per trillion by its share of 0.3. What is Well A's contribution to the blend?
  5. Multiply Well B's level of 2 parts per trillion by its share of 0.7. What is Well B's contribution to the blend?
  6. Add the two contributions from problems 4 and 5. What is the blended PFOA level in parts per trillion?
  7. A student adds 12 and 2, divides by 2, and reports 7 parts per trillion. How many parts per trillion higher is that than the blended level of 5.0 from problem 6?
  8. Peckhaven must bring the blend from 5.0 parts per trillion down to 4.0 parts per trillion. What is the percent decrease from 5.0 to 4.0?
  9. Peckhaven cuts Well A to 200 gallons per minute and raises Well B to 800 gallons per minute, keeping 1,000 gallons per minute in all. Using 12 and 2 parts per trillion for the two wells, what is the new blended level?
  10. Compare your answer to problem 9 with the 4.0 limit. Explain whether the new pumping plan works and why shifting flow to Well B lowers the blend.

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: 1,000 gallons per minute.
    Add the two well flows: 300 + 700 = 1,000 gallons per minute.
  2. Answer: 0.3.
    Divide Well A's flow by the total: 300 / 1,000 = 0.3, which is the fraction 3/10.
  3. Answer: 0.7.
    Divide Well B's flow by the total: 700 / 1,000 = 0.7, which is the fraction 7/10.
  4. Answer: 3.6 parts per trillion.
    Multiply the level by the share: 12 x 0.3 = 3.6 parts per trillion.
  5. Answer: 1.4 parts per trillion.
    Multiply the level by the share: 2 x 0.7 = 1.4 parts per trillion.
  6. Answer: 5.0 parts per trillion.
    Add the two contributions: 3.6 + 1.4 = 5.0 parts per trillion.
  7. Answer: 2.0 parts per trillion.
    The plain average is (12 + 2) / 2 = 7. Subtract the blended value: 7 - 5.0 = 2.0 parts per trillion too high. The average is wrong because it treats the small well as though it supplied half the water.
  8. Answer: 20 percent.
    The drop needed is 5.0 - 4.0 = 1.0. Divide by the starting level: 1.0 / 5.0 = 0.20, which is 20 percent.
  9. Answer: 4.0 parts per trillion.
    The new shares are 200 / 1,000 = 0.2 and 800 / 1,000 = 0.8. Then 12 x 0.2 = 2.4 and 2 x 0.8 = 1.6, and 2.4 + 1.6 = 4.0 parts per trillion.
  10. Answer: The new plan meets the limit exactly.
    The blend lands at 4.0 parts per trillion, which is at the maximum contaminant level rather than above it. Shifting flow to Well B lowers the blend because the blended level is a weighted result, so raising the share carried by the cleaner well pulls the total down. Peckhaven would still want a margin below the limit, since one well can go offline.

Differentiation

Support

Give students a two-row table for the fictional Peckhaven blend with the columns "flow," "share," "level," and "contribution," and complete the Well A row together before problem 4. Students who confuse the share with the level can be asked to check that the two shares add to 1 before multiplying.

Extension

Ask students to find the largest flow, in gallons per minute, that the fictional Well A could contribute while keeping the blend at or below 3.5 parts per trillion, with the total still at 1,000 gallons per minute. Students should set up an equation rather than testing values one at a time.

ELL supports

Preteach "blend," "share," and "level" using two labeled jars of colored water poured into one pitcher, and connect the color of the mixture to the blended number for the town of Peckhaven. Provide the sentence frame for problem 10: "The plan works because the blend is ____, and shifting flow to Well B lowers the blend because ____."

Extensions

Students can look up whether their own water system reports PFOA results in its annual water quality report, then use the fictional Peckhaven method to predict what a blend of two of those sources would produce. A second follow-on asks students to model a third well and explain how the weighted calculation changes when three shares must add to 1.