Mixture Problems

混合 Mixture

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Three types of mixture problem

• Type A: Calculate final concentration

• Type B: Increase or decrease concentration

• Type C: Find recipe . i.e. How to mix two solutions.

Multiple Choice

Pre-Question 1: "3 gallons of a 20% sugar solution is mixed with 5 gallons of a 50% sugar solution. What is the concentration of the mixture?"

Which type of question is this? (45 secs)

• Type A: Calculate final concentration.

• Type B: Change concentration

• Type C: Find the recipe

Multiple Choice

Question 1: 3 gallons of a 20% sugar solution is mixed with 5 gallons of a 50% sugar solution. What is the concentration of the mixture? (Poll, 3 mins)

• 30%

• 40%

• 41.875%

• 38.75%

Calculate concentration problem is straight forward.

Multiple Choice

Question 2: 100 mL of a 12% saline solution is mixed with 250 mL of an 18% saline solution. What is the concentration of the resulting mixture? (3 miins)

• 14.1%

• 16.3%

• 22.5%

• 18%

Multiple Choice

Pre Question 3 : "How many quarts of a 75% sugar solution must be mixed with 3 quarts of a 10% sugar solution to make a 60% solution?"

Which type of question is this?

• Type A: Calculate final concentration.

• Type B: Change concentration

• Type C: Find the recipe

In general, Type B question requires an algebraic approach. But it actually can be solved arithmetically.

Arithmatical apporach

• Hypotactically, we assume that final solution can be separated into original 3 quarts of solution with increase concentration and added unknown quarts of solution with decreased concentration.

• Sugar gained in the 3 quarts should be Sugar lost in the unknown quarts.

Let's calculate

Multiple Choice

Question 3: How many quarts of a 75% sugar solution must be mixed with 3 quarts of a 10% sugar solution to make a 60% solution?

• 15 quarts

• 10 quarts

• 9 quarts

• 5 quarts

Multiple Choice

Question 5: How many pounds of nuts costing $2.50 per pound should be mixed with 2 pounds of nuts costing $3.50 per pound to obtain a mixture costing $3.00 per pound? (30 second, use your gut feeling)

• 6 lb

• 15 lb

• 2 lb

• 1.5 lb

What's your gut feeling?

• To mix $2.50/lb cheap nuts with $3.50/lb expansive nuts to get $3.00/lb priced nuts?

• We need to mix: Half & Half

Multiple Choice

Pre Question 6 : "Jenny wants to make 13 L of a 52% acid solution by mixing together a 56% acid solution and a 43% acid solution. How much of each solution must she use?"

Which type of question is this?

• Type A: Calculate final concentration.

• Type B: Change concentration

• Type C: Find the recipe

How to solve Type C problem? Find receipt to mix two solutions.

• Algebraic

• Trial and Error

• Gut Feeling (e.g. Half & Half)

• Number Sense(e.g. Gain Lost balance)

Extend your "half&half" intuition

• To mix 43% and 56% solution to get 52% solution, I would like to ask

• Is 52% more close to 43% or 56%?

Open Ended

Pre Question 6: What's the concentration increase from 43% to 52% and what's the concentration decrease from 56% to 52%? (Open ended, automatic full score with any input)

Double check your calculation

• Concentration increase=52%-43%=9%

• Concentration decrease=56%-52%=4%

Poll

Pre-Question 6: Jenny wants to make 13 L of a 52% acid solution by mixing together a 43% acid solution and a 56% acid solution. How much of each solution must she use? (Polling Question. Not scored/Automatic Full Score)

• 9 L of 43% solution, 4 L of 56% solution

• 4 L of 43% solution, 9 L of 56% solution

Number Sense

• Small concentration changes means more volume participation 

• Big concentration changes means less volume participation

• So that we can still have

• Sugar Gain=Sugar Loss

Multiple Choice

Redo if you don't get in the first run.

Question 6: Jenny wants to make 13 L of a 52% acid solution by mixing together a 43% acid solution and a 56% acid solution. How much of each solution must she use?

• 9 L of 43% solution, 4 L of 56% solution

• 4 L of 43% solution, 9 L of 56% solution