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Practice set b

A bag contains only nickels and dimes. The value of the collection is $2. If there are 26 coins in all, how many of each coin are there?

There are 14 dimes and 12 nickels.

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Sample set c (mixture problems)

A chemistry student needs 40 milliliters (ml) of a 14% acid solution. She had two acid solutions, A and B, to mix together to form the 40 ml acid solution. Acid solution A is 10% acid and acid solution B is 20% acid. How much of each solution should be used?

Step 1: Let x = number of ml of solution A . y = number of ml of solution B .

Step 2:  There are two relationships.
     (a) The sum of the number of ml of the two solutions is 40.
        x + y = 40

     (b) To determine the second equation, draw a picture of the situation.
      A label 'Quantities on this row' pointing to three beakers representing the equation x plus y is equal to forty. The first beaker is labeled as x with a plus sign between the first and second beakers. The second beaker is labeled as y with an equal sign between the second and third beakers. The third beaker is labeled as 40. A second label 'Rates on this row' has an arrow pointing to three labels below the three beakers. The first label is 'point ten,' the second label is 'point twenty,' and the third label is 'point fourteen.'
      The equation follows directly from the drawing if we use the idea of amount times quantity.

Step 3: .10 x + .20 y = .14 ( 40 ) { x + y = 40 .10 x + .20 y = .14 ( 40 ) ( 1 ) ( 2 ) { x + y = 40 .10 x + .20 y = .14 ( 40 ) ( 1 ) ( 2 )
 Solve this system by addition. First, eliminate decimals in equation 2 by multiplying both sides by 100.

      { x + y = 40 10 x + 20 y = 14 ( 40 ) ( 1 ) ( 2 )
 Eliminate x by multiplying equation 1 by 10 and then adding.

      10 x 10 y = 400 10 x + 20 y = 560 10 y = 160 y = 16 Then, x + 16 = 40 x = 24 x = 24 , y = 16

Step 4:  24 ml and 16 ml to add to 40 ml.
      10 ( 24 ) + 20 ( 16 ) = 560 Is this correct? 240 + 320 = 560 Is this correct? 560 = 560 Yes, this is correct .
 The solution checks.

Step 5:  The student should use 24 ml of acid solution A and 16 ml of acid solution B.

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Practice set c

A chemistry student needs 60 ml of a 26% salt solution. He has two salt solutions, A and B, to mix together to form the 60 ml solution. Salt solution A is 30% salt and salt solution B is 20% salt. How much of each solution should be used?

The student should use 36 ml of salt solution A and 24 ml of salt solution B.

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Exercises

The sum of two numbers is 22. One number is 6 more than the other. What are the numbers?

The two numbers are 14 and 8.

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The sum of two numbers is 32. One number is 8 more than the other. What are the numbers?

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The difference of two numbers is 12 and one number is three times as large as the other. Whatare the numbers?

The two numbers are 18 and 6.

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The difference of two numbers is 9 and one number is 10 times larger than the other. Whatare the numbers?

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Half the sum of two numbers is 14 and half the difference is 2. What are the numbers?

The numbers are 16 and 12.

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One third of the sum of two numbers is 6 and one fifth of the difference is 2. What are the numbers?

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A 14 pound mixture of grapes sells for $ 3.10 . Type 1 grape sells for 25¢ a pound and type 2 grape sells for 20¢ a pound. How many pounds of each type of grape were used?

6 pounds of Type 1 and 8 pounds of Type 2.

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The cost of 80 liters of a blended cleaning solution is $28. Type 1 solution costs 20¢ a liter and type 2 solution costs 40¢ a liter. How many liters of each solution were used to form the blended solution?

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The cost of 42 grams of a certain chemical compound is $ 14.40 . Type 1 chemical costs 45¢ a gram and type 2 chemical costs 30¢ a gram. How many grams of each chemical were used to form the compound?

12 grams of Type 1 and 30 grams of Type 2.

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A play was attended by 342 people, some adults and some children. Admission for adults was $ 1.50 and for children 75¢. How many adults and how many children attended the play?

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200 tickets were sold to a college’s annual musical performance. Tickets for students were $ 2.50 and for nonstudents $ 3.50 . The total amount collected was $537. How many nonstudents purchased tickets for the performance?

37 non-student tickets.

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A chemistry student needs 22 ml of a 38% acid solution. She has two acid solutions, A and B, to mix together to form the solution. Acid solution A is 40% acid and acid solution B is 30% acid. How much of each solution should be used?

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A chemistry student needs 50 ml of a 72% salt solution. He has two salt solutions, A and B, to mix together to form the solution. Salt solution A is 60% salt and salt solution B is 80% salt. How much of each solution should be used?

30 ml of 80% solution; 20 ml of 60% solution.

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A chemist needs 2 liters of an 18% acid solution. He has two solutions, A and B, to mix together to form the solution. Acid solution A is 10% acid and acid solution B is 15% acid. Can the chemist form the needed 18% acid solution? (Verify by calculation.) If the chemist locates a 20% acid solution, how much would have to be mixed with the 10% solution to obtain the needed 2-liter 18% solution?

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A chemist needs 3 liters of a 12% acid solution. She has two acid solutions, A and B, to mix together to form the solution. Acid solution A is 14% acid and acid solution B is 20% acid. Can the chemist form the needed 12% solution? (Verify by calculation.) If the chemist locates a 4% acid solution, how much would have to be mixed with the 14% acid solution to obtain the needed 3-liter 12% solution?

( a )  cannot form 12% solution; ( b ) 3 5  liter of 4% solution .

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A chemistry student needs 100 ml of a 16% acid solution. He has a bottle of 20% acid solution. How much pure water and how much of the 20% solution should be mixed to dilute the 20% acid solution to a 16% acid solution?

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A chemistry student needs 1 liter of a 78% salt solution. She has a bottle of 80% salt solution. How much pure water and how much of the 80% salt solution should be mixed to dilute the 80% salt solution to a 78% salt solution?

25 ml of pure water; 975 ml of 80% salt solution.

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A parking meter contains 42 coins. The total value of the coins is $ 8.40 . If the meter contains only dimes and quarters, how many of each type are there?

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A child’s bank contains 78 coins. The coins are only pennies and nickels. If the value of the coins is $ 1.50 , how many of each coin are there?

18 nickels; 60 pennies.

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Exercises for review

( [link] ) Find the product: ( 3 x 5 ) 2 .

9 x 2 30 x + 25

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( [link] ) Find the difference: 2 x 1 x 2 + x 6 x + 2 x 2 + 5 x + 6 .

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( [link] ) Use the substitution method to solve { 4 x y = 3 2 x 5 y = 15

( 0 , 3 )

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( [link] ) Use the addition method to solve { 3 x + 4 y = 7 4 x 5 y = 1

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Questions & Answers

How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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