Math problem set Grade 7 Math

Marrow Creek Filter Plant's Backwash Costs: A Problem Set

A grade 7 problem set where students calculate a filter plant's backwash water use and cost, mixing decimals and fractions in every step.

Grade: Grade 7
Subject: Math
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

7.EE.B.3 Common Core Math

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically, and assess the reasonableness of answers using mental computation and estimation strategies.

How this material aligns: Students combine a fractional backwash duration, a decimal per-gallon water cost, and a fractional reclaimed-water share into one multistep calculation, mixing decimals and fractions exactly as this standard requires.

All materials for 7.EE.B.3 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-16.

Objectives

Students will solve a multistep problem combining decimals and fractions to find water volume and cost.
Students will apply a fractional reclaimed-water share to find a reduced cost.

Vocabulary

Backwash: Backwash is when a treatment plant reverses the flow of water through a filter to flush out the dirt and particles it has trapped. It is like rinsing out a dirty sponge so the filter can keep working well.

Also: reclaimed water, unit conversion

Teacher overview

Marrow Creek Filter Plant (a fictional treatment plant used for this problem set) periodically "backwashes" its filters, running clean water backward through the filter media to flush out trapped particles, and every gallon used in that process costs the plant money even though it never reaches a customer. This problem set walks students through finding the volume and cost of one backwash cycle, scaling that cost up to a full week, and then applying a fraction that represents water the plant reclaims and reuses instead of paying for again. A common misconception in this math is multiplying the per-minute backwash rate by the fraction of an hour without first converting that fraction to minutes, which produces a volume many times too small.

Marrow Creek Filter Plant's Backwash Costs: A Problem Set — Grade 7 Math

Name: ____________________________ Date: ______________

Problems

Marrow Creek Filter Plant (a fictional treatment plant used for this problem set) runs its backwash process on the schedule described below.

Marrow Creek backwashes one filter for 3/4 of an hour at a time. Convert 3/4 of an hour to minutes.
During the backwash, water flows at a rate of 480 gallons per minute. Using your answer to problem 1, find the total gallons used in one backwash cycle.
Marrow Creek pays $0.85 for every 1,000 gallons of treated water it uses. Find the cost of one backwash cycle, using your answer to problem 2.
The plant runs this backwash cycle an average of 2.5 times per day. Find the total gallons used for backwashing in one day.
Find the daily cost of backwashing, using your answer to problem 4 (or problem 3 multiplied by 2.5).
Find the weekly cost of backwashing, assuming the plant backwashes every day of the week.
Marrow Creek reclaims 1/3 of each cycle's backwash water, piping it to a settling basin for reuse instead of paying for it again. What fraction of each cycle's water does the plant still pay for as "new" water?
Using the fraction from problem 7, find the plant's new weekly backwash cost after accounting for the reclaimed water.
How many dollars per week does reclaiming the backwash water save Marrow Creek? Use your answers to problems 6 and 8.

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: 45 min.
3/4 of an hour × 60 minutes per hour = 45 minutes.
Answer: 21,600 gal.
480 gallons per minute × 45 minutes = 21,600 gallons.
Answer: $18.36.
21,600 gallons ÷ 1,000 = 21.6 (thousands of gallons). 21.6 × $0.85 = $18.36.
Answer: 54,000 gal.
21,600 gallons × 2.5 cycles = 54,000 gallons.
Answer: $45.90.
54,000 gallons ÷ 1,000 = 54 (thousands of gallons). 54 × $0.85 = $45.90, which matches $18.36 × 2.5 = $45.90.
Answer: $321.30.
$45.90 per day × 7 days = $321.30.
Answer: 2/3.
The plant reclaims 1/3 of the water, so it still pays for the remaining fraction: 1 − 1/3 = 2/3.
Answer: $214.20.
The volume paid for is 2/3 of the original: 21,600 × 2/3 = 14,400 gallons per cycle, so the new weekly cost is $321.30 × 2/3 = $214.20.
Answer: $107.10.
$321.30 − $214.20 = $107.10 saved per week.

Differentiation

Support (below grade level)

Provide a step-by-step calculation chart with labeled blanks for minutes, gallons per cycle, cost per cycle, gallons per day, and cost per day, so students fill in one value at a time rather than setting up the whole chain themselves. Allow a calculator for every step.

Extension (above grade level)

Ask students to find what fraction of backwash water Marrow Creek would need to reclaim to cut its weekly backwash cost in half, using the weekly cost you calculated in problem 6 as the starting point.

ELL supports

Provide a labeled diagram of the backwash process showing water flowing backward through the filter and a portion of it being piped to a settling basin for reuse, with the words "backwash," "reclaim," and "cycle" defined next to the diagram. Allow students to complete the calculation chart from the Support section instead of writing full sentences.