Use ratios to find concentrations, blends, and mixture amounts
What Are Mixture Problems?
Mixture problems ask you to combine two or more things (solutions, prices, ingredients) and find the resulting concentration, cost, or ratio.
The Key Principle
Amount of "stuff" before mixing = Amount of "stuff" after mixing.
If you mix juice and water, the total amount of actual juice doesn't change — it just gets distributed in a larger volume.
Examples
Mix 2 liters of 30% juice with 3 liters of 60% juice. What's the final concentration?
Juice in solution 1: 2 × 0.30 = 0.6 liters
Juice in solution 2: 3 × 0.60 = 1.8 liters
Total juice: 0.6 + 1.8 = 2.4 liters
Total volume: 2 + 3 = 5 liters
Concentration: 2.4 ÷ 5 = 48%
A store mixes $5/lb coffee with $8/lb coffee in a 2:3 ratio. What's the blend price per pound?
Cost of cheap: 2 × $5 = $10
Cost of premium: 3 × $8 = $24
Total cost: $10 + $24 = $34
Total pounds: 2 + 3 = 5
Price per pound: $34 ÷ 5 = $6.80/lb
Strategy
💡 For every mixture problem:
1. Find the amount of the "key ingredient" in each part
2. Add them up
3. Divide by the total quantity
The answer should always fall between the two starting values — a sanity check.
🎯 Practice Problems
1. Mix 4L of 20% salt solution with 6L of 50% salt solution. What percent salt is the mixture?
A) 35%
B) 38%
C) 40%
D) 45%
2. Mix 3 lbs of $4/lb candy with 2 lbs of $9/lb candy. What is the price per pound?
A) $5.50
B) $6.00
C) $6.50
D) $7.00
3. 5L of 10% juice mixed with 5L of 30% juice gives what concentration?
A) 15%
B) 20%
C) 25%
D) 40%
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🎯 Bonus Practice
1. How much 80% solution must be added to 10L of 20% solution to get 50% solution?
A) 5L
B) 10L
C) 15L
D) 20L
2. A paint mix is 3 parts red and 5 parts white. You need 24 liters total. How much red?
A) 6L
B) 8L
C) 9L
D) 12L
3. Mix equal parts of 40% acid and 60% acid. What's the concentration?
A) 45%
B) 50%
C) 55%
D) 100%
4. $6/lb nuts mixed with $10/lb nuts in a 1:3 ratio. Price per pound?
A) $7
B) $8
C) $9
D) $16
5. You mix 8L of 25% solution with 2L of pure water (0%). What is the new concentration?