SOLUTION: You have 10 cups of a cleaning solution that is 10% white vinegar and 90% water. You want the mixture to be 20% white vinegar and 80% water. How many cups of white vinegar do you n

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: You have 10 cups of a cleaning solution that is 10% white vinegar and 90% water. You want the mixture to be 20% white vinegar and 80% water. How many cups of white vinegar do you n      Log On

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Question 1072131: You have 10 cups of a cleaning solution that is 10% white vinegar and 90% water. You want the mixture to be 20% white vinegar and 80% water. How many cups of white vinegar do you need to add to the mixture?
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, amount of white vinegar to add

%2810%2A10%2B100%2Ax%29%2F%28x%2B10%29=20

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%2810%2B10x%29%2F%28x%2B10%29=2
10%2B10x=2x%2B20
8x=10
x=10%2F8=5%2F4=1%261%2F4





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fixed mistake

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
You have 10 cups of a cleaning solution that is 10% white vinegar and 90% water. You want the mixture to be 20% white vinegar
and 80% water. How many cups of white vinegar do you need to add to the mixture?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let x be the volume of white vinegar you need to add to the mixture (measured in cups).

Then the amount of the pure vinegar in the mixture will be (10*0.1 + x) cups.

The volume of liquid will be 10 + x.

The concentration equation is

%2810%2A0.1+%2B+x%29%2F%2810%2Bx%29 = 0.2.

Multiply both sides by (10+x) and then simplify. You will get

1 + x = 0.2x + 2,

x - 0.2x = 2 - 1  --->  0.8x = 1  --->  x = 1%2F0.8%7D%7D+=+%7B%7B%7B10%2F8 = 1.25.

Answer.  you need to add 1.25 of a cup of the pure vinegar to the mixture.

Check.  0.1%2A10+%2B+1.25%29%2F%2810%2B1.25%29 = 2.25%2F11.25 = 0.2.  Correct !

Solved.

The solution by "josgarithmetic is WRONG.


There is entire bunch of lessons covering various types of mixture problems
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Word problems on mixtures for antifreeze solutions
    - Word problems on mixtures for alloys
    - Typical word problems on mixtures from the archive
in this site.

Read them and become an expert in solution the mixture word problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Mixture problems


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

You have 10 cups of a cleaning solution that is 10% white vinegar and 90% water. You want the mixture to be 20% white vinegar and 80% water. How many cups of white vinegar do you need to add to the mixture?
Correct amount of vinegar to add: highlight_green%28matrix%281%2C2%2C+1.25%2C+cups%29%29