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Mixture word problems worksheets

Model ten concentration, alloy, food-mixture, and unit-cost stories with exact linear equations. Every sheet covers five equation families and reports both ingredient amounts when two quantities are unknown.

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Read the story, identify the requested quantity and show your reasoning. Include the correct unit in your answer.

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Conserve the component, then solve

Define x with its unit, then equate the exact amount of sugar, salt, acid, clay, metal, peanuts, gold or total cost before and after mixing. Liquid percentages are by volume under the stated additive-volume model; the other mixture percentages are by mass.

Each key keeps exact fractional values through the conservation check, rounds final values once to the nearest hundredth, and labels both ingredient amounts when the story asks how much of each to use.

Learning objective

What this activity builds

Translate a mixture story into an exact conservation equation, solve for the requested percentage, mass, volume, or unit cost, and verify the original quantities.

Worked example

How much 25% silver alloy and 79% silver alloy make 6 lb of 34% silver alloy?

Let x be pounds of the 25% alloy. 25x + 79(6 − x) = 34(6), so x = 5 lb and 6 − x = 1 lb.

The two masses total 6 lb, and their exact silver masses must equal the silver mass in the target alloy.

Teaching notes

Make the practice count

  • State whether a percentage is by mass or by volume.
  • Define x as the first ingredient amount before writing T − x.
  • Keep exact fractions through the conservation check and round only the displayed final answer.

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Math SheetNameScoreTeacherDateMixture Word ProblemsDefine x, write an exact conservation equation, solve without rounding intermediate values, and give exact answers plus nearest-hundredth values in the requestedunit. Percentages in liquid stories are by volume; other mixture percentages are by mass.1. How many pounds of a 72% silver alloy and a 21% silver alloy are needed to make 8 lb at 62% silver by mass?2. 5 L of a 74% vinegar solution is mixed with 11 L of a 30% vinegar solution. Assuming volumes add, what is the mixture's vinegar percentage byvolume?3. 13 mL of one acid solution is mixed with 6 mL of a 48% acid solution. Assuming volumes add, the mixture is 76% acid by volume. Find the firstsolution's acid percentage by volume.4. 16 mL of one salt solution is mixed with 18 mL of a 71% salt solution. Assuming volumes add, the mixture is 79% salt by volume. Find the firstsolution's salt percentage by volume.math-sheet.comPage 1 / 3
Math SheetNameScoreTeacherDateMixture Word ProblemsDefine x, write an exact conservation equation, solve without rounding intermediate values, and give exact answers plus nearest-hundredth values in the requestedunit. Percentages in liquid stories are by volume; other mixture percentages are by mass.5. How many pounds of a 58% peanut mix and a 22% peanut mix are needed to make 18 lb at 39% peanuts by mass?6. 11 oz of soil containing 70% clay by mass is mixed with 14 oz containing 44% clay by mass. What percentage clay by mass is in the mixture?7. A 5 lb apple mixture is 62% red apples by mass. It is combined with 20 lb that is 46% red apples by mass. What percentage of the combined mass isred apples?8. A starting alloy is 53% gold by mass. What mass of this alloy should be combined with 12 g of pure gold to produce an alloy that is 91% gold by mass?math-sheet.comPage 2 / 3
Math SheetNameScoreTeacherDateMixture Word ProblemsDefine x, write an exact conservation equation, solve without rounding intermediate values, and give exact answers plus nearest-hundredth values in the requestedunit. Percentages in liquid stories are by volume; other mixture percentages are by mass.9. A trail mix combines 19 lb of peanuts at $4/lb, 3 lb of raisins at $3/lb, and 7 lb of cashews at $4/lb. What is the exact unit cost of the mixture, and what isit to the nearest hundredth of a dollar per pound?10. 5 L of cranberry juice is mixed with 16 L of apple juice containing 6% sugar. Under an ideal additive-volume model, the final mixture is 9% sugar byvolume. What was the cranberry juice sugar percentage by volume?math-sheet.comPage 3 / 3

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