Weighted averages and mixtures

Grade 9 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   Ari mixes 10 L of 10% juice with x L of 40% juice to make a 20% blend. Which equation fits?

   • 0.10(10) + 0.40x = 0.20x
   • 0.10(10) + 0.40x = 0.20(10)
   • 0.10(10) + 0.40x = 0.20(10 + x)
   • 0.10x + 0.40(10) = 0.20(10 + x)
2. 2.

   Pia mixes 6 L of 20% syrup with x L of 50% syrup to make a 30% blend. Which equation fits?

   • 0.20x + 0.50(6) = 0.30(6 + x)
   • 0.20(6) + 0.50x = 0.30x
   • 0.20(6) + 0.50x = 0.30(6)
   • 0.20(6) + 0.50x = 0.30(6 + x)
3. 3.

   Noah mixes x mL of 5% salt water with 40 mL of 25% salt water to make a 10% blend. Which equation fits?

   • 0.05(40) + 0.25x = 0.10(x + 40)
   • 0.05x + 0.25(40) = 0.10(x + 40)
   • 0.05x + 0.25(40) = 0.10x
   • 0.05x + 0.25(40) = 0.10(40)
4. 4.

   Quizzes 30%, project 20%, final 50%. Scores so far: quizzes 84, project 90. Bo wants a final grade of 88. Which equation finds the final exam score s?

   • 0.30(84) + 0.20(90) + 0.50s = 88
   • 0.30(84) + 0.20(90) + s = 88
   • 0.50(84) + 0.30(90) + 0.20s = 88
   • (84 + 90 + s) ÷ 3 = 88
5. 5.

   Tests 40%, project 60%. Score so far: tests average 78. Esme wants a final grade of 90. Which equation finds the project score p?

   • 0.40(78) + 0.60p = 90
   • 0.40(78) + p = 90
   • 0.60(78) + 0.40p = 90
   • (78 + p) ÷ 2 = 90
6. 6.

   Lab 20%, quizzes 30%, exam 50%. Scores so far: lab 92, quizzes 80. Luz wants a final grade of 86. Which equation finds the exam score e?

   • 0.20(92) + 0.30(80) + e = 86
   • 0.20(92) + 0.30(80) + 0.50e = 86
   • 0.50(92) + 0.20(80) + 0.30e = 86
   • (92 + 80 + e) ÷ 3 = 86
7. 7.

   Kira mixes 3 L of 20% juice with 1 L of 60% juice. Which blend percent is reasonable, and why?

   • 30%: between 20 and 60, closer to 20 because 3 of the 4 liters are 20%.
   • 15%: a blend is weaker than both juices it is made from.
   • 80%: the percents add up when two juices are mixed together into one blend.
   • 40%: the middle of 20 and 60, since the two juices are simply mixed together.
8. 8.

   Zee mixes 2 L of 10% juice with 6 L of 50% juice. Which blend percent is reasonable, and why?

   • 30%: the middle of 10 and 50, since the two juices are simply mixed together.
   • 40%: between 10 and 50, closer to 50 because 6 of the 8 liters are 50%.
   • 60%: the percents add up when two juices are mixed together into one blend.
   • 5%: a blend is weaker than both juices it is made from.
9. 9.

   A grade counts a quiz of 70 once and a project of 90 three times. Jun finds the weighted grade. Which result is reasonable, and why?

   • 80: the middle of 70 and 90, since there are just two scores to average together.
   • 95: a grade can be above both scores when one counts more.
   • 85: between 70 and 90, closer to 90 because the project counts 3 times.
   • 160: the two scores add up in a weighted grade, so the grade is their sum.
10. 10.

    Milo mixes 1 kg of $8 nuts with 4 kg of $3 raisins. Which price per kg is reasonable, and why?

    • $2: a mix costs less than both foods it is made from.
    • $4: between $3 and $8, closer to $3 because 4 of the 5 kg are $3.
    • $5.50: the middle of $3 and $8, since the two foods are simply mixed together.
    • $11: the prices add up when the two foods are mixed together into one bag.