Weighted averages and mixtures

Grade 9 Math Worksheet - Challenge Me

Circle the best answer.

1. 1.

   Homework 40%, exam 60%. Plan B: homework 70%, exam 30%. Pia: homework 98, exam 76. Esme compares the two plans for Pia's scores. Which plan gives the higher grade, and by how much?

   • Plan B, by 6.6 points: 91.4 against 84.8.
   • Plan A, by 6.6 points: 89.2 against 82.6.
   • Plan A, by 6.6 points: 91.4 against 84.8.
   • Neither: the plain average, 87, is the same for both plans.
2. 2.

   Lab 25%, exam 75%. Plan B: lab 50%, exam 50%. Ren: lab 70, exam 96. Tala compares the two plans for Ren's scores. Which plan gives the higher grade, and by how much?

   • Plan B, by 6.5 points: 89.5 against 83.
   • Neither: the plain average, 83, applies to both plans.
   • Plan A, by 6.5 points: 89.5 against 83.
   • Plan B, by 6.5 points: 83 against 76.5.
3. 3.

   Table. Liters of 40% juice added (x): 0, 5, 10, 30. Blend percent: 10, 20, 25, 32.5. Pia mixes 10 L of 10% juice with x L of 40% juice and records the blend percent. Which statement does the table support?

   • The blend stays near 10%, because most of the juice is the 10% juice.
   • The blend rises 2 points per liter added, so it climbs at a steady rate.
   • The blend passes 40% once x is large enough, because the amount of strong juice keeps growing.
   • The blend keeps rising with x, but more slowly each time, and stays below 40%.
4. 4.

   Table. Liters of 30% brine added (x): 0, 10, 20, 60. Blend percent: 10, 16.7, 20, 25. Jun mixes 20 L of 10% brine with x L of 30% brine and records the blend percent. Which statement does the table support?

   • The blend keeps rising toward 30%, but slows down and never passes it.
   • The blend rises 0.67 points per liter added, so it reaches 30% at 30 liters.
   • The blend stays near 10%, because the tank started as 10% brine.
   • The blend passes 30% once x is large enough, because more strong brine keeps being added.
5. 5.

   Jun drives 60 miles at 30 mph, then 60 miles at 60 mph. What is the average speed for the whole 120 miles?

   • 40 mph
   • 90 mph
   • 50 mph
   • 45 mph
6. 6.

   Ari buys $40 of gas at $4 per gallon, then $40 of gas at $5 per gallon. What is the average price per gallon?

   • $9.00
   • $4.44
   • $4.56
   • $4.50
7. 7.

   A class of 12 students averages 80. A class of 18 students averages 70. Bo finds the average of all 30 students. What is it?

   • 76
   • 75
   • 150
   • 74
8. 8.

   Luz has a 30% acid cleaner and plain water (0% acid). How many liters of cleaner and of water make 12 L of 20% acid?

   • 2.4 L of cleaner and 9.6 L of water
   • 6 L of cleaner and 6 L of water
   • 4 L of cleaner and 8 L of water
   • 8 L of cleaner and 4 L of water
9. 9.

   Kira mixes $6 per kg nuts with $3 per kg raisins to make 10 kg worth $4.20 per kg. How many kg of nuts are in the mix?

   • 5 kg
   • 6 kg
   • $42
   • 4 kg
10. 10.

    Esme needs 40 L of 22% solution from 10% and 30% stock. There are 20 L of the 30% stock. Is the mix possible?

    • Yes: it needs 20 L of each stock, and 20 L are available.
    • Yes: it needs 8.8 L of the 30% stock, and 20 L are available.
    • Yes: it needs 16 L of the 30% stock, and 20 L are available.
    • No: it needs 24 L of the 30% stock, but 20 L are available.