Question

a. exercises
complete the following tables.

	amount of mixture	percent of salt	amount of salt
2.	( x ) lb	65%
3.	90 oz	( 8% )
4.	15 g		4.95 g
5.		18%	14.4 l

	number of items	value per item	total value
7.	( n )	$5.31

	amount of mixture	percent of ingredient	amount of ingredient
9.	( x )	50%
10.	( x + 80 )	25%

make a table to help you answer each question.

1. if 10 gal of a 12% salt solution are mixed with 8 gal of an 80% salt solution, how much of the final solution do you have? how much salt is in the final solution? what percent of the final solution is salt?
2. if 4 gal of pure ethanol are added to 46 gal of 2% ethanol, how much of the final solution do you have? how much ethanol is contained in the mixture? what is the strength (percentage) of the ethanol in the mixture?
3. if you dilute 35 gal of a 40% acid solution with 7 gal of water, what is the amount and the strength of the mixture?
4. if you boil 3 gal of 10% salt water until there are only 2 gal left, what is the percent of salt when you finish?
5. mr. harper, the candy store manager, wants to mix butterscotch candies and cinnamon balls to make a deluxe mix to sell for $3/lb. butterscotch candy sells for $3.40/lb and the cinnamon balls sell for $2.90/lb. how many pounds of each should he use to make 20 lb of the mix?
6. how much cream that is 30% butterfat must be mixed with milk that is 1% butterfat to make 45 gal of cream that is 12% butterfat?
7. mr. li owns a tea company and wants to make an exotic blend of tea. he has two brands to mix. one brand is an indian tea that sells for $3.25/lb. the other is a chinese tea that sells for $4/lb. if he wants to make 35 lb that will sell for $3.70/lb, how many pounds of each should he mix?
8. chase has 3 gal of a solution that is 30% antifreeze that he wants to use to winterize his car. how much pure antifreeze should he add to this solution to produce a solution that is 65% antifreeze?
9. how many gallons of pure water must be added to 10 gal of 30% salt water to make a solution that is 25% salt water?

Explanation:

First Table (Salt Mixtures)

Step1: Calculate salt amount

$\text{Amount of Salt} = 20 \times 70\% = 20 \times 0.7 = 14$ gal

Step2: Calculate salt amount

$\text{Amount of Salt} = x \times 65\% = 0.65x$ lb

Step3: Calculate salt amount

$\text{Amount of Salt} = 90 \times 8\% = 90 \times 0.08 = 7.2$ oz

Step4: Calculate salt percentage

$\text{Percent of Salt} = \frac{4.95}{15} \times 100\% = 33\%$

Step5: Calculate mixture amount

$\text{Amount of Mixture} = \frac{14.4}{18\%} = \frac{14.4}{0.18} = 80$ L

Step1: Calculate total value

$\text{Total Value} = 20 \times 1.26 = 25.20$

Step2: Calculate total value

$\text{Total Value} = n \times 5.31 = 5.31n$

Step1: Calculate ingredient amount

$\text{Amount of Ingredient} = 80 \times 20\% = 80 \times 0.2 = 16$ L

Step2: Calculate ingredient amount

$\text{Amount of Ingredient} = x \times 50\% = 0.5x$

Step3: Calculate ingredient amount

$\text{Amount of Ingredient} = (x+80) \times 25\% = 0.25(x+80) = 0.25x + 20$

Answer:

1. 14 gal
2. $0.65x$ lb
3. 7.2 oz
4. 33%
5. 80 L

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Second Table (Total Value)