Weighted averages and mixtures

Grade 9 Math Worksheet - Challenge Me

Circle the best answer.

1. 1.

   Tests 30%, project 70%. Plan B: tests 60%, project 40%. Kira: tests 95, project 80. Zee compares the two plans for Kira's scores. Which plan gives the higher grade, and by how much?

   • Neither: the plain average, 87.5, is the same for both plans.
   • Plan A, by 4.5 points: 90.5 against 86.
   • Plan A, by 4.5 points: 89 against 84.5.
   • Plan B, by 4.5 points: 89 against 84.5.
2. 2.

   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 A, by 6.6 points: 89.2 against 82.6.
   • Plan B, by 6.6 points: 91.4 against 84.8.
   • Plan A, by 6.6 points: 91.4 against 84.8.
   • Neither: the plain average, 87, is the same for both plans.
3. 3.

   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 A, by 6.5 points: 89.5 against 83.
   • Plan B, by 6.5 points: 89.5 against 83.
   • Plan B, by 6.5 points: 83 against 76.5.
   • Neither: the plain average, 83, applies to both plans.
4. 4.

   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 keeps rising with x, but more slowly each time, and stays below 40%.
   • The blend passes 40% once x is large enough, because the amount of strong juice keeps growing.
   • The blend rises 2 points per liter added, so it climbs at a steady rate.
5. 5.

   Table. Cups of water added (x): 0, 2, 8, 24. Blend percent: 50, 40, 25, 12.5. Noah adds x cups of water (0% juice) to 8 cups of 50% juice and records the blend percent. Which statement does the table support?

   • The blend keeps falling as water is added, more slowly each time, but never reaches 0%.
   • The blend drops below 0% once enough water is added, because water has no juice.
   • The blend stays at 50%, because water adds no juice to the cup.
   • The blend falls 5 points per cup, so it reaches 0% at 10 cups.
6. 6.

   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 passes 30% once x is large enough, because more strong brine keeps being added.
   • The blend stays near 10%, because the tank started as 10% brine.
   • 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.
7. 7.

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

   • 50 mph
   • 45 mph
   • 40 mph
   • 90 mph
8. 8.

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

   • $4.44
   • $9.00
   • $4.50
   • $4.56
9. 9.

   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 16 L of the 30% stock, and 20 L are available.
   • Yes: it needs 8.8 L of the 30% stock, and 20 L are available.
   • No: it needs 24 L of the 30% stock, but 20 L are available.
   • Yes: it needs 20 L of each stock, and 20 L are available.
10. 10.

    A course grade is w times homework plus (1 - w) times final. Ren's homework is 90, final is 70, and the grade is 82. What is the weight w on homework?

    • 40%
    • 50%
    • 60%
    • 12%