Worksheet Grade 10 Math

Merrivale Well Blend: Meeting the 4 ppt PFAS Limit

A grade 10 worksheet on PFAS: students blend two fictional wells, size treatment removal, and write an equation to meet the 4.0 ppt federal limit.

Grade: Grade 10
Subject: Math
Material: Worksheet
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

HSA-CED.A.1 Common Core Math

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

How this material aligns: Item 5 has students write and solve a one-variable equation for the blend fraction that brings two wells to exactly the 4.0 ppt limit.

All materials for HSA-CED.A.1 →

HSN-Q.A.1 Common Core Math

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

How this material aligns: Items 6 and 7 carry ppt, percent, and the MGD-to-gpm conversion through multi-step work, choosing and interpreting units consistently as this standard requires.

All materials for HSN-Q.A.1 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will compute blended contaminant concentrations from two sources using a weighted average.
Students will write and solve an equation for the blend ratio that meets a regulatory limit.

Vocabulary

PFAS: A large family of human-made chemicals used in things like nonstick pans, waterproof fabric, and firefighting foam. They are called forever chemicals because they take a very long time to break down.
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.
Maximum contaminant level (MCL): A maximum contaminant level, or MCL, is the highest amount of a certain substance that federal rules allow in drinking water. Water systems test regularly to prove their water stays under each limit.

Also: blending

Teacher overview

PFAS are long-lasting chemicals that federal rules now limit in drinking water. The maximum contaminant level for PFOA is 4.0 parts per trillion, and water systems must comply by April 2029. In May 2026 EPA proposed letting eligible systems apply for a two-year exemption, to April 2031; the proposal would not change the 4.0 ppt limit and was not yet final as of September 2026. This worksheet uses the fictional town of Merrivale, whose two wells test at different PFOA levels. Teaching note: remind students that blending is a weighted average, so the result always lands between the two source values, never below the cleaner one.

Merrivale Well Blend: Meeting the 4 ppt PFAS Limit — Grade 10 Math

Name: ____________________________ Date: ______________

Student Worksheet

The town of Merrivale has two drinking-water wells. This scenario is fictional, and its numbers are set for this worksheet.

Well data for PFOA:

Well 6: 9.0 ppt
Well 9: 1.0 ppt
Federal limit (maximum contaminant level): 4.0 ppt

Well 6 tests at 9.0 ppt. How many ppt above the 4.0 ppt limit is that?
A granular carbon filter removes 90 percent of the PFOA from Well 6 (a value set for this worksheet). What is the treated concentration in ppt?
Does the treated Well 6 water from item 2 meet the 4.0 ppt limit? Explain in one sentence.
The town blends Well 6 (9.0 ppt) and Well 9 (1.0 ppt) in equal amounts, with no treatment. Find the blended PFOA concentration, then state whether it meets the limit.
Let x be the fraction of the blend that comes from Well 6. Write an equation for a blend of exactly 4.0 ppt, then solve for x and give both wells' percents.
The town needs 1.0 MGD total at the item 5 blend. Using 1 MGD = 694 gpm, find the flow from each well in gpm.
Without blending, what is the minimum percent removal a filter must reach on raw Well 6 water (9.0 ppt) to meet the 4.0 ppt limit?
Federal PFAS rules are still being revised. Explain why a town might design treatment for a target lower than 4.0 ppt today.

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

Answer Key

Answer: 5.0 ppt.
9.0 ppt - 4.0 ppt = 5.0 ppt above the limit.
Answer: 0.9 ppt.
Removing 90 percent leaves 10 percent: 9.0 x (1 - 0.90) = 9.0 x 0.10 = 0.9 ppt.
Answer: Yes.
At 0.9 ppt the treated water is below the 4.0 ppt limit, so it meets the standard.
Answer: 5.0 ppt.
An equal blend is the average: (9.0 + 1.0) / 2 = 5.0 ppt. That is above 4.0 ppt, so the equal blend does not meet the limit.
Answer: x = 0.375 (37.5 percent Well 6, 62.5 percent Well 9).
The blend equation is 9x + 1(1 - x) = 4. That gives 8x + 1 = 4, so 8x = 3 and x = 0.375. Well 6 is 37.5 percent and Well 9 is 62.5 percent.
Answer: 260 gpm from Well 6, 434 gpm from Well 9.
1.0 MGD = 694 gpm. Well 6: 0.375 x 694 = 260.25, about 260 gpm. Well 9: 0.625 x 694 = 433.75, about 434 gpm. The two round to a total near 694 gpm.
Answer: 56 percent.
Removal needed is (9.0 - 4.0) / 9.0 x 100 = 5 / 9 x 100 = 55.6, or about 56 percent.
Answer: A stricter target leaves a safety margin if the rule tightens or a well worsens.
Because PFAS rules and compliance dates are still being revised, designing to a lower target avoids costly rework and protects against a well's level rising over time.

Differentiation

Support

Provide the weighted-average setup for item 5 already framed as 9x + 1(1 - x) = 4, so students focus on solving rather than building the equation. Allow a calculator and a number line showing that any blend must fall between 1.0 and 9.0.

Extension

Have students find the blend fraction that would meet a stricter 2.0 ppt target instead of 4.0 ppt, then explain what that stricter goal does to how much of the cleaner well the town must use.

ELL supports

Pre-teach "blend," "parts per trillion," and "limit" with a two-cup mixing demonstration. Provide sentence frames for item 3, "The treated water meets the limit because ___," and item 8, "A town might aim below 4.0 ppt because ___."