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I am having very difficult times in understanding the following and related mixture problems.Can anybody guide me the easy and nice trick that is useful in understanding,visualizing and solving these types of problems? following are few of those.

  • How many liters of a 70% alcohol solution must be added to 50 liters of a 40% alcohol solution to produce a 50% alcohol solution?

  • How many ounces of pure water must be added to 50 ounces of a 15% saline solution to make a saline solution that is 10% salt?

  • Find the selling price per pound of a coffee mixture made from 8 pounds of coffee that sells for \$9.20 per pound and 12 pounds of coffee that costs \$5.50 per pound?

  • How many pounds of lima beans that cost $0.90 per pound must be mixed with 16 pounds of corn that costs \$0.50 per pound to make a mixture of vegetables that costs \$0.65 per pound?

  • Two hundred liters of a punch that contains 35% fruit juice is mixed with 300 liters (L) of another punch. The resulting fruit punch is 20% fruit juice. Find the percent of fruit juice in the 300 liters of punch?

  • Ten grams of sugar are added to a 40-g serving of a breakfast cereal that is 30% sugar. What is the percent concentration of sugar in the resulting mixture?

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3 Answers 3

up vote 2 down vote accepted

Let's consider $1$st problem.

Problem:

  • How many liters of a 70% alcohol solution must be added to 50 liters of a 40% alcohol solution to produce a 50% alcohol solution?

"Easy and nice trick" :)

Let's consider liquids separately: alcohol - alcohol; water - water.   Then image:

Solutions

Then one can write equation for each liquid:

for alcohol: $$\qquad 0.7 \cdot x + 0.4 \cdot 50 = 0.5 \cdot (x+50);\tag{1}$$

or for water: $$\qquad 0.3 \cdot x + 0.6 \cdot 50 = 0.5 \cdot (x+50).\tag{2}$$

Then solve $(1)$ (or $(2)$ ) :

$$ 0.2\cdot x=5; $$ $$ x=25 \mbox{ (liters)}. $$

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Here are the set-up for 4 out of these questions. You can use these guides to complete the rest:

Let $x$ = the amount in liter of the $70%$ alcohol solution, then by equating the amount of alcohol before and after mix the 1st equation is:

$0.7x + 0.4*50 = .5(x + 50)$

Let $x$ be the amount of pure water in ounces, then the 2nd equation is: $0*x + 0.15*50 = 0.1(x + 50)$

Let $x$ be the percent of concentration of sugar in the resulting mix, the equation is: $10 + 0.3*40 = 50x$

Let $x$ be the amount in pounds of lima beans, then the equation is: $0.9x + 0.5*16 = 0.65(x + 16)$

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The first one: Let $x$ be amount of $70%$ sol. It boils down to $70x+40*50=(x+50)50$ because in total you will have $x+50$ liters of liquid. Do you see how? Give the others a try yourself and show your work so we can help

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I do not need solutions they exist on many sites What I need is a general strategy. –  khan Mar 26 at 18:27
    
The equation I provided in the first line is the strategy. I want you to translate that equation in words! –  imranfat Mar 26 at 18:28

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