Math problem set Grade 6 Math

Dunmore Water Blend: Mixing Ratios and Mineral Decimals

A grade 6 problem set on a fictional town blending well and river water, using mixing ratios, percent, and decimals to track dissolved minerals per gallon.

Grade: Grade 6
Subject: Math
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator (optional)

Standards

6.RP.A.3 Common Core Math

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations, including finding a percent of a quantity and converting measurement units.

How this material aligns: Problems 1 through 3 use the two-part-to-three-part blend ratio and percent of the blend, the ratio and percent reasoning about equivalent quantities this standard targets.

All materials for 6.RP.A.3 →

6.NS.B.3 Common Core Math

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

How this material aligns: Problems 4 through 10 multiply and subtract decimal gram-per-gallon mineral amounts, such as 300 times 0.3 and 0.30 minus 0.22, the multi-digit decimal fluency this standard expects.

All materials for 6.NS.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 2026-07-23.

Objectives

Students will use a mixing ratio to find how much well and river water are in a blend.
Students will multiply and subtract decimals to find the minerals per gallon of a blend.

Vocabulary

Key words: ratio, percent, decimal, minerals, blend

Teacher overview

Some towns mix water from two sources to get a better balance of minerals. In Dunmore, the river water carries more dissolved minerals than the well water, so blending them lowers the mineral amount in each gallon. In many places the reverse is true, because groundwater picks up minerals from the rock it moves through. This problem set follows the town of Dunmore, a fictional town, and moves from mixing ratios to decimal amounts of minerals per gallon. A common mistake to watch for is finding the average of the two mineral amounts without weighting it by how much of each water is in the blend; the blend here is not equal parts.

Dunmore Water Blend: Mixing Ratios and Mineral Decimals — Grade 6 Math

Name: ____________________________ Date: ______________

Problems

Use these numbers for the whole set. The town of Dunmore blends 2 parts well water to 3 parts river water. River water carries 0.3 gram of dissolved minerals per gallon. Well water carries 0.1 gram of dissolved minerals per gallon.

Write the ratio of well water to river water in simplest form.
What percent of the blend is well water, and what percent is river water?
The plant makes 500 gallons of blend. How many gallons are well water, and how many are river water?
How many grams of minerals come from the 300 gallons of river water in that blend?
How many grams of minerals come from the 200 gallons of well water in that blend?
What is the total mineral mass in the 500-gallon blend?
What is the mineral amount per gallon of the finished blend?
River water by itself has 0.3 gram per gallon. By how much does blending lower the minerals per gallon?
Explain why Dunmore blends well water with the river water instead of using river water alone.
Suppose the town changed the recipe to equal parts, 1 part well water to 1 part river water. What would the minerals per gallon be then?

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: 2 : 3. The recipe is 2 parts well to 3 parts river, which is already in simplest form.
Answer: 40 percent well and 60 percent river. Well is 2 of 5 parts (2 ÷ 5 = 40 percent); river is 3 of 5 parts (3 ÷ 5 = 60 percent).
Answer: 200 gallons well and 300 gallons river. 500 × (2 ÷ 5) = 200 well; 500 × (3 ÷ 5) = 300 river.
Answer: 90 grams. 300 gallons × 0.3 gram per gallon = 90 grams.
Answer: 20 grams. 200 gallons × 0.1 gram per gallon = 20 grams.
Answer: 110 grams. 90 grams from the river water + 20 grams from the well water = 110 grams.
Answer: 0.22 gram per gallon. 110 grams ÷ 500 gallons = 0.22 gram per gallon.
Answer: 0.08 gram per gallon. 0.30 gram − 0.22 gram = 0.08 gram per gallon lower.
Answer: Well water carries fewer minerals, so mixing it with the river water lowers the minerals in each gallon, giving softer water than the river alone.
Answer: 0.2 gram per gallon. With equal parts, each gallon is half river (0.3) and half well (0.1): (0.3 + 0.1) ÷ 2 = 0.2 gram per gallon.

Differentiation

Support

Give students a picture of 5 jugs, 2 labeled "well" and 3 labeled "river," so the 2 : 3 ratio is visible before they compute. Provide the gallon split (200 and 300) already found for items 4 and 5 so they can focus on the decimal multiplication.

Extension

Ask students to find the minerals per gallon if the recipe changed to 3 parts well water to 2 parts river water, then explain why that blend is even softer than the 2 : 3 recipe. Have them show the full decimal work.

ELL supports

Pre-teach "blend," "minerals," "well water," and "river water" with a labeled drawing of two sources flowing into one tank. Provide a sentence frame for item 9: "Dunmore blends the two because well water has ___ minerals." Allow the jug drawing as shown work.