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Grade 9 · Math · Algebra 1

9th grade Weighted averages and mixtures worksheet

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Weighted averages and mixtures

Grade 9 Math Worksheet

NameDate

Circle the best answer.

  1. Ari mixes 12 L of 15% juice with x L of 45% juice to make a 25% blend. How many liters x of the 45% juice are needed?

    • 6 L
    • 18 L
    • 24 L
    • about 2.7 L

  2. Pia mixes 12 L of 20% syrup with x L of 70% syrup to make a 30% blend. How many liters x of the 70% syrup are needed?

    • about 1.7 L
    • 48 L
    • 15 L
    • 3 L

  3. Noah mixes 9 L of 10% green paint with x L of 40% green paint to make a 20% blend. How many liters x of the 40% paint are needed?

    • 13.5 L
    • 18 L
    • 4.5 L
    • 2.25 L

  4. Tala mixes 20 mL of 5% salt water with x mL of 35% salt water to make a 15% blend. How many milliliters x of the 35% water are needed?

    • 30 mL
    • about 5.7 mL
    • 40 mL
    • 10 mL

  5. Pia needs 20 L of 26% solution from 20% stock and 50% stock. How many liters of the 50% stock?

    • 5.2 L
    • 4 L
    • 16 L
    • 10 L

  6. Bo needs 12 kg of nut mix worth $5 per kg, made from $4 nuts and $7 nuts. How many kg of the $7 nuts?

    • $60
    • 4 kg
    • 6 kg
    • 8 kg

  7. Zee needs 40 mL of 18% solution from 10% stock and 30% stock. How many mL of the 30% stock?

    • 24 mL
    • 20 mL
    • 16 mL
    • 7.2 mL

  8. Current work 70%, final exam 30%. Current work average: 88. Ren wants a final grade of 90. What final exam score is needed, and is it possible (scores top out at 100)?

    • Possible: the final needs to be about 94.7.
    • Possible: a final score of 28.4 works.
    • Possible: a final score of about 90.9 works.
    • Possible: a final score of 92 works.

  9. Skills 30%, quizzes 30%, final 40%. Skills: 84. Quizzes: 92. Luz wants a final grade of 90. What final score is needed, and is it possible (scores top out at 100)?

    • Possible: the final needs to be 93.
    • Possible: a final score of 94 works.
    • Possible: a final score of 96 works.
    • Possible: a final score of 37.2 works.

  10. Projects 60%, exam 40%. Projects average: 85. Tala wants a final grade of 92. What exam score is needed, and is it possible (scores top out at 100)?

    • Not possible: the exam would need to be 102.5.
    • Possible: an exam score of 41 works.
    • Possible: an exam score of 99 works.
    • Possible: an exam score of about 96.7 works.
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9th grade Weighted averages and mixtures worksheet – printable
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About this worksheet

Weighted averages and mixtures. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can write an equation from a mixture story: pure juice in equals pure juice out, and the blend holds both amounts.
  • I can write a weighted-grade equation for the score I still need and decide whether it is possible under a 100 cap.
  • I can read a table of blend percent against amount added, and see the rise slow down without passing the stronger juice.
  • I can find an average speed or price when the weights are time or gallons, not the number of trips.

Standard: N-Q.A.2 (partial), A-CED.A.1

Words to know

weight: How many times, or how much, a score counts in the final grade.

weighted average: An average where some parts count more than others.

mixture: Two amounts put together, like two juice drinks in one jug.

blend: The mixture you get; its percent is between the two you mixed.

pure amount: The juice (or paint, or salt) alone: amount × percent.

stock: A solution you already have, like 20% syrup.

Common mistakes

Your child left the added amount out of the blend's total.

Your child left the first amount out of the blend's total.

Your child attached each percent to the wrong amount.

What to say

Ask: how many liters are in the blend, the first amount plus the new one?

Ask: how many liters are in the blend, the first amount plus the new one?

Ask: which percent belongs with the first amount?

Questions parents ask

What is the most common mistake with weighted averages and mixtures?

Your child left the added amount out of the blend's total.

How can I help my child with weighted averages and mixtures?

Ask: how many liters are in the blend, the first amount plus the new one?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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