Weighted averages and mixtures

Grade 9 Math Worksheet - Challenge Me

Circle the best answer.

1. 1.

   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.
   • Neither: the plain average, 83, applies to both plans.
   • Plan B, by 6.5 points: 89.5 against 83.
   • Plan B, by 6.5 points: 83 against 76.5.
2. 2.

   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 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 keeps falling as water is added, more slowly each time, but never reaches 0%.
   • The blend falls 5 points per cup, so it reaches 0% at 10 cups.
3. 3.

   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 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.
4. 4.

   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
   • 50 mph
   • 90 mph
   • 45 mph
5. 5.

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

   • $4.50
   • $9.00
   • $4.56
   • $4.44
6. 6.

   Milo hikes 3 km uphill at 2 km/h, then 3 km downhill at 6 km/h. What is the average speed for the 6 km?

   • 3 km/h
   • 5 km/h
   • 8 km/h
   • 4 km/h
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?

   • 74
   • 150
   • 76
   • 75
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?

   • 6 kg
   • $42
   • 5 kg
   • 4 kg
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%