1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
IrinaVladis [17]
3 years ago
14

John wants to make a 100 ml of 6% alcohol solution mixing a quantity of a 3% alcohol solution with an 8% alcohol solution. What

are the quantities of each of the two solutions (3% and 8%) he has to use?
Mathematics
1 answer:
mart [117]3 years ago
3 0

Answer:

-50 ml of 3% alcohol solution and 150 ml of 8% alcohol solution

Step-by-step explanation:

For us to solve this type of mixture problem, we must represent the problem in equations. This will be possible by interpreting the question.

Let the original volume of the first alcohol solution be represented with x.

The quantity of the first alcohol solution needed for the mixture is 3% of x

                   ⇒ \frac{3}{100} * x

                       = 0.03x

Let the original volume of the second alcohol solution be represented with y.

The quantity of the second alcohol solution needed for the mixture is 5% of y

                   ⇒ \frac{5}{100} * y

                       = 0.05y

The final mixture of alcohol solution is 6% of 100 ml

                 ⇒ \frac{6}{100} * 100 ml

                       = 6 ml

Sum of values of two alcohol solutions = Value of the final mixture

                     0.03x + 0.05y = 6 ml               ..........(1)

Sum of original quantity of each alcohol solution = Original volume of the of mixture

                     x + y = 100 ml                          ..........(2)      

For easy interpretation, I will be setting up a table to capture all information given in the question.

Component                       Unit Value      Quantity(ml)       Value

3% of Alcohol solution        0.03                 x                     0.03x

8% of Alcohol solution        0.08                 y                     0.08y

Mixture of 100ml of 6%        0.06               100                       6    

                                                                x + y = 100       0.03x + 0.08y =6

Looking at the equations we derived, we have two unknowns in two equations which is a simultaneous equation.

                                0.03x + 0.05y = 6 ml               ..........(1)

                                x + y = 100 ml                           ..........(2)    

Using substitution method to solve the simultaneous equation.

Making x the subject of formula from equation (2), we have,

                                x  = 100 - y                                 ..........(3)

Substituting  x  = 100 - y from equation (3) into equation (1)

                               0.03(100 - y) + 0.05y = 6  

                               3 - 0.03y + 0.05y = 6  

Rearranging the equation,            

                               0.05y - 0.03y = 6 - 3

                               0.02y = 3

                               y = \frac{3}{0.02}

                               y = 150 ml

Substituting y = 150 ml into equation (3) to get x

                              x  = 100 - 150 ml

                              x = - 50 ml

The quantity of the first alcohol solution needed for the mixture for 3% is - 50 ml

The quantity of the second alcohol solution needed for the mixture for 5% is 150 ml

This solution means 50 ml of the first alcohol solution must be removed from the mixture with 150 ml of the second alcohol solution to get a final mixture of 100 ml of 6% alcohol solution.

You might be interested in
❗️URGENT NEED ASAP❗️
kipiarov [429]

Answer:

Step-by-step explanation:

❗️URGENT NEED ASAP❗️

Given functions,

f(x) = -5x – 14 g(x) = -02 + 9x - 1

find f(9) + g(-2)

6 0
3 years ago
Read 2 more answers
Janice’s twin sister, Janette, is also working to save money over the summer. She is in college and needs $1,000 for her books f
valina [46]

Answer:

A. It will take 13 weeks until she gets the money nd she will have $50 left!

Step-by-step explanation:

Please mark brainliest! Have a nice day!

4 0
3 years ago
a train leaves from new york to chicago at 60mph. ANother train leaves from Chicago to New York at 40 mph. How far apary are the
Nutka1998 [239]

Answer:

100 miles

Step-by-step explanation:

Relative Speed: 60+40=100 mph

you can think that one train is stationary,another one is 100 mph

so one hour before the train pass each other,the distance is 100 miles

3 0
3 years ago
A cube has a volume of 1,000 cubic feet. What is the edge length of<br> the cube?
Komok [63]

Answer:

10

Step-by-step explanation:

The volume of a cube is equal to its (side length)^3

so s^3 = 1000

s=\sqrt[3]{1000} =10

6 0
3 years ago
Read 2 more answers
If y = -6cosx, what is the amplitude?
aniked [119]

 

\displaystyle\bf\\y=-6cos\,x\\\\\textbf{is equivalent to:}\\\\y=6cos(x+\pi)\\\\\textbf{where 6 is the maximum value or amplitude}\\\\\implies~~~\boxed{\bf~amplitude=6}

 

8 0
3 years ago
Other questions:
  • Solve 2√3+3√7 adding fraction
    14·1 answer
  • How to solve linear equations 12 = y + (-2)
    13·2 answers
  • Year Value 2004 $8000 2005 $12,000 2006 $16,000 2007 $20,000 2008 $24,000 The table shows the value of Susie's bank account duri
    9·2 answers
  • Circle O is shown below. The diagram is not drawn to scale? If Angle r is 32, what is angle O?
    5·1 answer
  • Here is my question: -7 times x = 189
    14·1 answer
  • Ifr=9 and t= 11, what is the value of 2rt?<br> 50<br> O 101<br> 100<br> O 198
    5·2 answers
  • HELP NOW!!?!! who ever gets all three of them right gets brainlist and (15 points) *questions in photo*
    5·1 answer
  • X + 84 2 -104 open or closed dot?​
    10·1 answer
  • Someone help me im trying not to fail this year-​
    5·2 answers
  • Sophia puts $450 in an account earning 7% simple interest annually. How many dollars will she
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!