Weighted averages and combined rates: Practice 1 (Foundation)

10 original teaching questions with answers and explanations.

Instructions for this set

Use the actual group size, time or unit count as the weight. A calculator is allowed. Do not assume equal weights unless stated.

Feedback mode has no time limit or negative marking. The optional timed challenge allows 15 minutes and uses the scoring shown on its rules screen. Those settings are not official assessment rules.

Practise with feedback Optional timed challenge

  1. 1. Ten staff average 30 checks each and twenty staff average 45. What is the combined average?
    1. 35
    2. 37.5
    3. 40
    4. 42.5

    Reference: q-e6e055d0-92 · Report this question

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    Answer: C. 40

    Total checks = 10 times 30 plus 20 times 45 = 1,200. Divide by 30 staff to obtain 40.
  2. 2. A shop sells 40 units at $12 and 60 units at $17. What is the average selling price per unit?
    1. $15.50
    2. $14.00
    3. $14.50
    4. $15.00

    Reference: q-e5565aec-94 · Report this question

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    Answer: D. $15.00

    Revenue is 480 plus 1,020 = $1,500 for 100 units. Average price is $15.
  3. 3. An assessment gives 30% weight to a score of 80 and 70% to a score of 60. What is the weighted score?
    1. 66
    2. 68
    3. 70
    4. 64

    Reference: q-4610143a-102 · Report this question

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    Answer: A. 66

    Weighted score = 0.30 times 80 plus 0.70 times 60 = 24 plus 42 = 66.
  4. 4. Eight trainees average 70 points and twelve average 85. What is the combined average?
    1. 77.5
    2. 79
    3. 80
    4. 76

    Reference: q-c82ab3dc-86 · Report this question

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    Answer: B. 79

    Total points = 8 times 70 plus 12 times 85 = 1,580. Divide by 20 trainees to get 79.
  5. 5. Twenty packages have an average mass of 6 kg. Five more packages average 10 kg. What is the new average?
    1. 8 kg
    2. 6.5 kg
    3. 6.8 kg
    4. 7 kg

    Reference: q-be7e8d61-105 · Report this question

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    Answer: C. 6.8 kg

    Combined mass = 20 times 6 plus 5 times 10 = 170 kg. Divide by 25 packages: 6.8 kg.
  6. 6. A group of 30 has an average score of 72. Ten members average 60. What is the average of the other twenty?
    1. 80
    2. 75
    3. 76
    4. 78

    Reference: q-5b0d7954-107 · Report this question

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    Answer: D. 78

    Total score = 2,160. Subtract the known 600 to leave 1,560 for twenty people: average 78.
  7. 7. A vehicle travels for one hour at 40 km/h and one hour at 60 km/h. What is its average speed?
    1. 50 km/h
    2. 52 km/h
    3. 60 km/h
    4. 48 km/h

    Reference: q-eca29d54-94 · Report this question

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    Answer: A. 50 km/h

    It travels 100 km in two hours. Total distance divided by total time gives 50 km/h.
  8. 8. A vehicle travels 60 km at 30 km/h and 60 km at 60 km/h. What is its average speed for the full journey?
    1. 50 km/h
    2. 40 km/h
    3. 45 km/h
    4. 48 km/h

    Reference: q-8cbbd427-105 · Report this question

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    Answer: B. 40 km/h

    The two stages take two hours and one hour. Average speed = total distance of 120 km divided by total time of three hours = 40 km/h.
  9. 9. A course score is 40% project and 60% exam. The project score is 75. What exam score gives an overall 81?
    1. 82
    2. 83
    3. 85
    4. 90

    Reference: q-8828de61-106 · Report this question

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    Answer: C. 85

    Project contributes 30 points. The exam must contribute 51, so its score is 51/0.60 = 85.
  10. 10. A batch mixes 30 litres of a 10% solution with 20 litres of a 25% solution. Assuming volumes add and concentrations are measured by volume, what is the final concentration?
    1. 17.5%
    2. 20%
    3. 15%
    4. 16%

    Reference: q-d3c81b1b-173 · Report this question

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    Answer: D. 16%

    The solute amounts are 3 and 5 litres. Eight litres in a 50-litre mixture gives 16%.

Review your method

Return to the weighted averages and combined rates lesson and identify the reasoning step behind each mistake before repeating the set.

Choose your practice difficulty

Difficulty labels describe the steps needed in these teaching sets; they are not validated ability bands. Start with foundation practice and move on after you can explain your method.

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