Worksheet Grade 10 Math

Corrindale Sands Desalter: Brine Load, Dilution, and Precision

A grade 10 worksheet using the pounds formula to find a fictional desalter brine strength, then solving a dilution equation and reporting at meter precision.

Grade: Grade 10
Subject: Math
Material: Worksheet
Time: 45 min
Prep: No prep
Materials: None

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: Items 5 and 6 have students create a one-variable equation for the dilution seawater flow that brings the fictional outfall to its permit limit, then solve that equation for the unknown flow.

All materials for HSA-CED.A.1 →

HSN-Q.A.3 Common Core Math

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

How this material aligns: Items 8 and 12 require students to report computed concentrations at the stated resolution of the plant meter rather than at the full precision of the arithmetic, and item 10 has them justify that choice in writing.

All materials for HSN-Q.A.3 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-09-04.

Objectives

Students will apply the pounds formula to find the dissolved solids load in each stream of a treatment plant.
Students will write and solve a one-variable equation for the dilution flow needed to meet a discharge limit.
Students will report computed concentrations at a precision that matches the measuring instrument.

Vocabulary

Total dissolved solids (TDS): Total dissolved solids is a measure of everything dissolved in water that you cannot see or filter out, like minerals and salts. Water with very high TDS can taste salty or bitter, even though it might look perfectly clear.
Brine: The extra-salty water left over after desalination pulls fresh water out of seawater. Plants must dispose of it carefully so it does not harm sea life.

Also: mass balance, dilution, significant figures

Teacher overview

The Corrindale Sands desalter, its outfall permit, and every flow and concentration on this worksheet are fictional. A seawater plant sends most of the salt it removes out through a brine stream, and the permit in this scenario caps the strength of what leaves the outfall, so the plant mixes brine with other water before discharge. Students track the dissolved solids with the pounds formula, solve for the dilution flow, and then decide how many digits the plant's meter can honestly support.

Corrindale Sands Desalter: Brine Load, Dilution, and Precision — Grade 10 Math

Name: ____________________________ Date: ______________

Student Worksheet

The Corrindale Sands desalter is fictional. It takes in 6.0 MGD of seawater at 34,000 mg/L of total dissolved solids. It produces 3.0 MGD of product water at 300 mg/L and 3.0 MGD of brine. The fictional outfall permit caps the mixed discharge at 40,000 mg/L. Use the pounds formula, which states that pounds per day equals concentration in mg/L times flow in MGD times 8.34.

Find the dissolved solids load in the feed seawater, in pounds per day, from 34,000 mg/L at 6.0 MGD.
Find the dissolved solids load in the product water, in pounds per day, from 300 mg/L at 3.0 MGD.
All of the solids that do not leave in the product water leave in the brine. Find the brine load in pounds per day.
The brine flow is 3.0 MGD. Find the brine concentration in mg/L.
The plant will blend the 3.0 MGD of brine with dilution seawater at 34,000 mg/L. Let d be the dilution flow in MGD. Write an equation in d that sets the mixed concentration equal to 40,000 mg/L.
Solve your equation for d. Round to the nearest hundredth.
Only 10.0 MGD of dilution seawater is available. Find the mixed concentration of the 3.0 MGD of brine and 10.0 MGD of seawater, to the nearest tenth of a mg/L.
The plant meter reads total dissolved solids to the nearest 100 mg/L. Report the item 7 value at that precision.
Does the item 8 value meet the 40,000 mg/L cap? Answer yes or no.
Explain why reporting the item 7 value with a tenths digit overstates what the meter can measure.
A second plan adds 4.0 MGD of reclaimed effluent at 900 mg/L to the 3.0 MGD of brine and the 10.0 MGD of seawater. Find the mixed concentration to the nearest tenth of a mg/L.
Report the item 11 value to the nearest 100 mg/L.
Does the item 12 value meet the 40,000 mg/L cap? Answer yes or no.

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: 1,701,360 pounds per day. The pounds formula gives 34,000 × 6.0 × 8.34, and 34,000 × 6.0 = 204,000, so 204,000 × 8.34 = 1,701,360 pounds per day.
Answer: 7,506 pounds per day. The pounds formula gives 300 × 3.0 × 8.34, and 300 × 3.0 = 900, so 900 × 8.34 = 7,506 pounds per day.
Answer: 1,693,854 pounds per day. Subtracting gives 1,701,360 − 7,506 = 1,693,854 pounds per day.
Answer: 67,700 mg/L. Rearranging the pounds formula gives concentration equal to 1,693,854 ÷ (3.0 × 8.34), and 3.0 × 8.34 = 25.02, so 1,693,854 ÷ 25.02 = 67,700 mg/L.
Answer: 67,700(3.0) + 34,000d = 40,000(3.0 + d). The left side is the total solids entering the mix, the right side is the same total at the permit concentration, and both sides use flow in MGD.
Answer: 13.85 MGD. Expanding gives 203,100 + 34,000d = 120,000 + 40,000d, so 83,100 = 6,000d and d = 13.85 MGD.
Answer: 41,776.9 mg/L. The combined solids are 203,100 + 340,000 = 543,100 and the combined flow is 13.0 MGD, so 543,100 ÷ 13.0 = 41,776.92, which rounds to 41,776.9 mg/L.
Answer: 41,800 mg/L. Rounding 41,776.9 to the nearest 100 gives 41,800 mg/L.
Answer: No. The reported 41,800 mg/L sits above the fictional permit cap of 40,000 mg/L, so 10.0 MGD of dilution water is not enough.
Answer: The meter cannot resolve tenths. Its smallest step is 100 mg/L, so the digits below that step come from the arithmetic rather than from any measurement. Reporting 41,776.9 mg/L suggests the plant knows the value to within a tenth, which no reading from that instrument can support.
Answer: 32,158.8 mg/L. The reclaimed effluent adds 900 × 4.0 = 3,600 units of solids, so the combined solids are 203,100 + 340,000 + 3,600 = 546,700 and the combined flow is 17.0 MGD, giving 546,700 ÷ 17.0 = 32,158.82, which rounds to 32,158.8 mg/L.
Answer: 32,200 mg/L. Rounding 32,158.8 to the nearest 100 gives 32,200 mg/L.
Answer: Yes. The reported 32,200 mg/L is below the fictional permit cap of 40,000 mg/L, so the second plan complies.

Differentiation

Support

Give students a filled-in mass balance table for the fictional plant with columns for stream, flow in MGD, concentration in mg/L, and pounds per day, with the feed row completed, so items 1 through 4 become a matter of extending the pattern. Provide the item 5 equation with only the 40,000 missing.

Extension

Ask students to find the largest brine flow the fictional plant could discharge with 10.0 MGD of dilution seawater while still meeting the 40,000 mg/L cap, then explain what that limit means for how much product water the plant can make. A further challenge is to redo item 7 assuming the seawater intake rises to 35,000 mg/L during a dry season and to state how much the mixed value shifts.

ELL supports

Provide a flow diagram of the fictional plant with three labeled arrows, feed, product, and brine, and the words concentration and load written beside a small worked example. Offer a sentence frame for item 10: "The meter measures to the nearest ___ mg/L, so digits smaller than that come from ___, not from ___."

Extensions

Have students compare the mixed discharge concentrations from items 7 and 11 with the seawater intake value of 34,000 mg/L and write a short note on which plan puts the smaller salt burden on the receiving water. A follow-on task is to sketch how the mixed concentration changes as the dilution flow rises from 5 to 20 MGD, using the fictional brine values from this worksheet.