Question 178471: please help with this question - it is from a review page my teacher made up.
White vinegar is available as a 5% acetic acid solution and a 10% acetic solution, by volume. How many millilitres of each solution must be mixed to make 100mL of a 7% solution.
I tried: Let x represent the amount of 5% vinegar.
Let y represent the amount of 10% vinegar.
These are the 2 equations I came up with, but my answer came out wrong.
x+y=100
100=x(0.05)+y(0.01)
The correct answer is supposed to be 60mL of 5% solution and 40mL of 10% solution.
Found 2 solutions by Mathtut, Alan3354:
Answer by Mathtut(3670)   (Show Source):
You can put this solution on YOUR website! White vinegar is available as a 5% acetic acid solution and a 10% acetic solution, by volume. How many millilitres of each solution must be mixed to make 100mL of a 7% solution.
I tried: Let x represent the amount of 5% vinegar.
Let y represent the amount of 10% vinegar.
These are the 2 equations I came up with, but my answer came out wrong.
x+y=100
100=x(0.05)+y(0.01)
The correct answer is supposed to be 60mL of 5% solution and 40mL of 10% solution.
:
x+y=100....eq 1
.05x+.1y=.07(100)
:
you were oh.........so close you forgot to multiply the final 100 ml solution by
:
7% and it should be .1y not .01y
:
I will let you carry it from here.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! White vinegar is available as a 5% acetic acid solution and a 10% acetic solution, by volume. How many millilitres of each solution must be mixed to make 100mL of a 7% solution.
I tried: Let x represent the amount of 5% vinegar.
Let y represent the amount of 10% vinegar.
These are the 2 equations I came up with, but my answer came out wrong.
x+y=100
100=x(0.05)+y(0.01)
The correct answer is supposed to be 60mL of 5% solution and 40mL of 10% solution.
-----------
x+y=100
100=x(0.05)+y(0.01) --> Make this 100*0.07 = 0.05x + 0.10y (not 0.01y)
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x+y=100
100*0.07 = 0.05x + 0.10y
0.05x + 0.10y = 7 --> 5x + 10y = 700
--------------
5x + 10y = 700
x + y = 100 --> y = 100-x
Sub into the 1st eqn
5x + 10*(100-x) = 700
5x + 1000-10x = 700
-5x = -300
x = 60
y = 40
Your approach was correct, but you overlooked one factor, the 100*0.07, and you had 1%, not 10%.
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