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Math problem set Grade 10 Math

Dunmoor Plant Fluoride and Alum Feed: The Pounds Formula

A grade 10 problem set where students compute chemical feed rates in pounds per day with the operator pounds formula and convert between mg/L, percent, and ppm.

Objectives

  1. Students will calculate chemical feed rates in pounds per day using dose, flow, and the 8.34 constant.
  2. Students will convert between mg/L, percent strength, and ppm.
  3. Students will explain how flow and dose each change the pounds-per-day feed.

Vocabulary

Key words: pounds formula, dose, flow, percent solution, feed rate

Teacher overview

Plant operators size chemical feeds with one workhorse equation, the pounds formula: pounds per day = dose in mg/L multiplied by flow in MGD multiplied by 8.34, the weight of a gallon of water in pounds. This set uses the fictional Dunmoor Water Treatment Plant to practice that formula for fluoride, alum, and chlorine, and to convert between the units operators actually record. A common misconception this set corrects is entering the flow in gallons per day instead of MGD; because in fresh water a mg/L is approximately one part per million, the formula expects flow in millions of gallons, so using raw gallons per day inflates the answer by a factor of a million.

Dunmoor Plant Fluoride and Alum Feed: The Pounds Formula — Grade 10 Math
Name: ____________________________ Date: ______________

Problems

Suppose the fictional Dunmoor Water Treatment Plant treats 3.0 MGD. Use the pounds formula for every feed: pounds per day = dose (mg/L) x flow (MGD) x 8.34. Also use these conversions: a 1 percent solution equals 10,000 mg/L, and in fresh water, like the water this plant treats, 1 mg/L is approximately equal to 1 ppm.

  1. The plant doses alum at 12 mg/L. Calculate the alum feed in pounds per day at the 3.0 MGD flow.
  2. The plant targets a fluoride dose of 0.7 mg/L. Calculate the fluoride feed in pounds per day at 3.0 MGD. Round to the nearest tenth.
  3. The plant doses chlorine at 2.5 mg/L. Calculate the chlorine feed in pounds per day at 3.0 MGD. Round to the nearest tenth.
  4. During a wet week, the flow rises to 5.0 MGD. Calculate the alum feed in pounds per day at the same 12 mg/L dose.
  5. A cleaning solution is labeled 2 percent available chlorine. Express that strength in mg/L using the conversion that a 1 percent solution equals 10,000 mg/L.
  6. Convert the plant's 0.7 mg/L fluoride residual to ppm.
  7. Your alum feed from problem 1 came out to 300.24 pounds per day, but the feed pump is set only in whole pounds per day. State the value rounded to the nearest whole pound.
  8. Alum costs $0.40 per pound in this scenario. Using the whole-pound feed from problem 7, calculate the daily alum cost.
  9. Over a 30-day month at that same whole-pound feed, how many pounds of alum does the plant use?
  10. Explain why doubling the flow in MGD while keeping the dose in mg/L constant doubles the pounds-per-day feed.

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: 300 lb/day. Feed = 12 x 3.0 x 8.34 = 300.24, about 300 pounds per day.
  2. Answer: 17.5 lb/day. Feed = 0.7 x 3.0 x 8.34 = 17.51, which rounds to 17.5 pounds per day.
  3. Answer: 62.6 lb/day. Feed = 2.5 x 3.0 x 8.34 = 62.55, which rounds to 62.6 pounds per day.
  4. Answer: 500 lb/day. Feed = 12 x 5.0 x 8.34 = 500.4, about 500 pounds per day.
  5. Answer: 20,000 mg/L. A 1 percent solution is 10,000 mg/L, so 2 percent is 2 x 10,000 = 20,000 mg/L.
  6. Answer: 0.7 ppm. The plant treats fresh water, where 1 mg/L is approximately equal to 1 ppm, so 0.7 mg/L is about 0.7 ppm.
  7. Answer: 300 lb/day. The computed 300.24 pounds per day rounds to 300 whole pounds per day, matching the pump's whole-pound setting.
  8. Answer: $120. Daily cost = 300 pounds x $0.40 per pound = $120.
  9. Answer: 9,000 lb. Over 30 days at 300 pounds per day, 300 x 30 = 9,000 pounds of alum.
  10. Answer: In the formula pounds per day = dose x flow x 8.34, the flow is a factor. Holding the dose and the 8.34 constant fixed while doubling the flow doubles the whole product, so the feed doubles.

Differentiation

Support

Provide the pounds formula with each slot labeled (dose, flow, constant) and one fully worked example before problem 1. Remind students to confirm the flow is written in MGD, not gallons per day, and allow a calculator.

Extension

Ask students to work the pounds formula backward: given a fluoride feed of 25 pounds per day at 3.0 MGD, solve for the dose in mg/L, and explain each step of the rearrangement.

ELL supports

Pre-teach "dose," "flow," "feed rate," and "solution strength" with a labeled diagram of a chemical feed pump in English and, where possible, students' home languages. Provide a units checklist so students confirm mg/L and MGD before multiplying.