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Mixture Word Problems Practice

Twelve hand-built mixture problems with full worked solutions. Each tracks one quantity — pure acid, pure salt, dollars of value, grams of alcohol — and sets the total before mixing equal to the total after.

  1. 1.

    How many liters of a acid solution should be mixed with liters of a solution to get a solution?

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  2. 2.

    How much pure water must be added to liters of a salt solution to make it ?

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  3. 3.

    How much pure antifreeze must be added to quarts of a mixture to raise it to ?

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  4. 4.

    A /lb nut blend is made from cashews at /lb and peanuts at /lb. For lb of blend, how much of each?

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    Let be pounds of cashews; peanuts are .

    lb cashews, lb peanuts.

  5. 5.

    A and a alcohol solution are combined to make L of a solution. How many liters of each?

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    Let be liters of ; the is .

    L of , L of .

  6. 6.

    How much of an copper alloy must be melted with kg of a alloy to get a alloy?

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  7. 7.

    A grocer mixes /lb candy with /lb candy to make lb worth /lb. How much of each?

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    Let be pounds of the candy; the other is .

    lb at , lb at .

  8. 8.

    How many liters of water must evaporate from L of a salt solution to make it ? (Salt stays.)

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    Salt is fixed at L. Let be liters removed.

  9. 9.

    A jar of nickels and dimes has coins worth . How many of each?

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    Let be nickels; dimes are .

    nickels, dimes.

  10. 10.

    A theater sells tickets, adults at and children at , for . How many of each?

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    Let be adult tickets; children are .

    adult, child.

  11. 11.

    is split between accounts paying and . The total annual interest is . How much is in each?

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    Let be the amount at ; the rest is .

    at , at .

  12. 12.

    A jar has twice as many dimes as quarters and is worth . How many of each?

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    Let be quarters; dimes are .

    quarters and dimes.
Written by
MPhil in Mathematics, Founder of Mathovia
Published

Mathematics verification: Mathematical formulas, calculations, worked examples and solutions are reviewed for accuracy before publication. How we check our work

Mixture Word Problems Practice

The Mixture Problems lesson covers percent solutions, dilutions, priced blends, and coins with a chart; this set is 12 problems to practice on, each fully solved.

How to use this set

For each problem, build a chart with a row per ingredient plus a mixture row, fill the pure-amount column as (quantity)(concentration), set the ingredient rows to sum to the mixture row, and solve. Then check. Type the amount into the box and press Check Answers. Where a problem asks how much of each, give both numbers separated by a comma — order does not matter, and units are ignored.

Common mistakes to watch for

Using percents instead of decimals.

Setting the target concentration outside the range of the two ingredients.

Forgetting that added water still increases the total quantity.

Adding concentrations directly instead of multiplying each by its amount first.

Where to go next

The setup is the Word Problems method with a chart; split-investment problems overlap with simple interest. If you prefer to clear the decimals first, that is the Linear Equations with Fractions Practice Problems skill. For every mixture type, see the Mixture Problems lesson.

Frequently Asked Questions

What is the general setup for a mixture problem?+

Track the pure amount of one ingredient. For each part, that amount is (quantity)(concentration). The sum across all parts equals (total quantity)(final concentration): .

Percents or decimals in the equation?+

Decimals. A solution contributes times its volume in pure substance.

How do I handle pure water or pure substance?+

Pure water is of the tracked substance, so its concentration is . Pure substance is , so its concentration is .

Are coin and ticket problems mixture problems?+

Yes. The 'concentration' is the value of each item, and you balance total count and total value. Split-investment problems use an interest rate as the concentration.

Why does an answer sometimes come out negative or larger than the total?+

The final concentration must lie between the two starting concentrations. You cannot mix and to get ; an impossible target produces an impossible answer.

Do I still add to the total quantity when I add pure water?+

Yes. Water's concentration term is , but the mixture's total quantity is still the original plus the water added.

How do I answer a "how much of each" question?+

Give both amounts separated by a comma. Order does not matter and units are ignored, so 20, 10 is accepted for twenty litres of one solution and ten of the other. Single-amount questions just take the one number.

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