SSAT Middle Level Quiz: Mixture And Comparison Problems
2 questions · exam conditions
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Mixture And Comparison ProblemsQuestion 1 of 2

A paint store mixes white paint with blue paint to create a custom color. White paint costs 25pergallonandbluepaintcosts25 per gallon and blue paint costs 35 per gallon. If 12 gallons of the mixture costs $$28 per gallon, what percentage of the mixture by volume is white paint?

White paint makes up 60% of the mixture by volume
White paint makes up 65% of the mixture by volume
White paint makes up 70% of the mixture by volume
White paint makes up 75% of the mixture by volume
White paint makes up 80% of the mixture by volume
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SSAT Middle Level Quiz

SSAT Middle Level Quiz: Mixture And Comparison Problems

Practice Mixture And Comparison Problems in SSAT Middle Level with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Mixture And Comparison Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for SSAT Middle Level.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A paint store mixes white paint with blue paint to create a custom color. White paint costs 25pergallonandbluepaintcosts25 per gallon and blue paint costs 35 per gallon. If 12 gallons of the mixture costs $$28 per gallon, what percentage of the mixture by volume is white paint?

  1. White paint makes up 60% of the mixture by volume
  2. White paint makes up 65% of the mixture by volume
  3. White paint makes up 70% of the mixture by volume (correct answer)
  4. White paint makes up 75% of the mixture by volume
  5. White paint makes up 80% of the mixture by volume
Explanation: When you encounter a mixture problem involving costs, you're dealing with a weighted average situation. The key insight is that the final price per gallon (28)fallsbetweenthetwocomponentprices(28) falls between the two component prices (25 and $35), and its position tells you the proportions. Let's say white paint makes up $xx fractionofthemixture,sobluepaintmakesupfraction of the mixture, so blue paint makes up (1−x)(1-x) $. The weighted average formula gives us: 25x + 35(1-x) = 28 Solving this equation: 25x + 35 - 35x = 28 -10x = -7 x = 0.7 = 70% We can verify: If 70% is white and 30% is blue, then 0.7(25) + 0.3(35) = 17.5 + 10.5 = 28 ✓ Answer A (60%) would give us 0.6(25) + 0.4(35) = 29 , which is too expensive. Answer B (65%) yields 0.65(25) + 0.35(35) = 28.5 , still too high. Answer D (75%) produces 0.75(25) + 0.25(35) = 27.25 , which is too cheap. Each wrong answer represents a common calculation error or misapplication of the weighted average formula. The correct answer is C: white paint makes up 70% of the mixture. Study tip: In mixture problems, always check that your answer makes intuitive sense. Since $28 is closer to $25 than to $35, you'd expect more white paint than blue paint in the mixture, which 70% white confirms.

Question 2

A tea merchant blends two types of tea. Type X costs 12perpoundandTypeYcosts12 per pound and Type Y costs 18 per pound. If he wants to create 25 pounds of a blend that costs $$15 per pound, and then sell it at a 20% markup, what will be his profit per pound?

  1. The profit per pound will be $$1.80
  2. The profit per pound will be $$2.40
  3. The profit per pound will be $$3.00 (correct answer)
  4. The profit per pound will be $$3.60
  5. The profit per pound will be $$4.20
Explanation: This problem combines two key concepts: mixture problems and profit calculations. When you see a blending scenario with different costs per unit, you need to set up equations based on both quantity and total cost. First, let's find how much of each tea type is needed. Let xx = pounds of Type X tea. Then (25−x)(25-x) = pounds of Type Y tea. The total cost equation is: 12x+18(25−x)=15(25)12x + 18(25-x) = 15(25). Solving: 12x+450−18x=37512x + 450 - 18x = 375, so −6x=−75-6x = -75 and x=12.5x = 12.5 pounds. This means 12.5 pounds of Type X and 12.5 pounds of Type Y. The blend costs 15perpoundtomake.Witha2015 per pound to make. With a 20% markup, the selling price is 15 × 1.20 = 18perpound.Therefore,profitperpound=sellingprice−cost=per pound. Therefore, profit per pound = selling price - cost =18 - 15 = 3.00$$. Choice A (1.80)representsonlythemarkupamountwithoutaddingittothebasecost.ChoiceB(1.80) represents only the markup amount without adding it to the base cost. Choice B (2.40) likely comes from incorrectly calculating 20% of 12insteadof12 instead of 15. Choice D ($$3.60) might result from taking 20% of $$18 (the selling price) instead of understanding that profit is the difference between selling price and cost. Remember that profit per unit equals selling price minus cost price. When dealing with percentage markups, always apply the percentage to the cost price to find the selling price, then subtract the original cost to find profit.