Question 275411: In a chemistry class, 6 liters of 4% silver iodide solution must be mixed with 10% solution to get a 6% solution. How many liters of 10% solution are needed?
Found 6 solutions by mananth, ikleyn, n2, josgarithmetic, greenestamps, math_tutor2020:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! In a chemistry class, 6 liters of 4% silver iodide solution must be mixed with 10% solution to get a 6% solution. How many liters of 10% solution are needed?
Let the quantity of 10% solution be x liters
4% solution------------------- 10% solution---------------- 6% solution ( mix)
6------------------------------- x ------------------------ (x+6) liters
0.04x + 0.1x = 0.06*(x+6)
0.14x= 0.06x+0.36
0.14x-0.06x=0.36
0.08x= 0.36
x= 0.36/0.08
= 4 liters
Answer by ikleyn(53729)  (Show Source):
You can put this solution on YOUR website! .
In a chemistry class, 6 liters of 4% silver iodide solution must be mixed with 10% solution to get a 6% solution.
How many liters of 10% solution are needed?
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The solution in the post by @mananth is incorrect starting from its first line to the end.
It is because his governing equation is written incorrectly.
I came to bring a correct solution.
Let x be the volume (in liters) of the 10% silver iodide solution to add.
Write the balance equation for solute (silver iodide)
0.04*6 + 0.1x = 0.06*(6+x).
Simplify and find x
0.24 + 0.1x = 0.36 + 0.06x,
0.1x - 0.06x = 0.36 - 0.24,
0.04x = 0.12
x = 0.12/0.04 = 3.
ANSWER. 3 liters of the 10% silver iodide solution should be added.
Solved correctly.
Answer by n2(77)  (Show Source):
You can put this solution on YOUR website! .
In a chemistry class, 6 liters of 4% silver iodide solution must be mixed with 10% solution to get a 6% solution.
How many liters of 10% solution are needed?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let x be the volume (in liters) of the 10% silver iodide solution to add.
Write the balance equation for solute (silver iodide)
0.04*6 + 0.1x = 0.06*(6+x).
Simplify and find x
0.24 + 0.1x = 0.36 + 0.06x,
0.1x - 0.06x = 0.36 - 0.24,
0.04x = 0.12
x = 0.12/0.04 = 3.
ANSWER. 3 liters of the 10% silver iodide solution should be added.
Solved correctly.
Answer by josgarithmetic(39782) (Show Source):
Answer by greenestamps(13320)  (Show Source):
You can put this solution on YOUR website!
The responses you have received so far all use the standard formal algebraic method for solving the problem -- writing and solving an equation which says the sum of the amounts of silver iodide in the two ingredients is equal to the amount in the mixture.
If a formal algebraic solution is needed, then that is the standard method and almost certainly the fastest formal method.
But 2-part mixture problems like this can be solved much faster using an informal method using the ratio of the amounts of the two ingredients.
Here in words is the solution to this problem using this method.
(1) The target 6% solution is "twice as close to 4% as it is to 10%" (the difference between 4% and 6% is 2%; the difference between 6% and 10% is 4%.)
(2) That means the amount of 4% silver iodide in the mixture must be twice as much as the amount of 10% silver iodide.
(3) The mixture uses 6 liters of the 4% silver iodide, so it must use 3 liters of the 10% silver iodide.
ANSWER: 3 liters
Answer by math_tutor2020(3835) (Show Source):
You can put this solution on YOUR website!
Tutor mananth made an error when writing 0.04x as it should be 0.04*6 instead.
Solving 0.04*6+0.1x = 0.06*(x+6) leads to x = 3 as tutor ikleyn has shown, and as I show below.
Tutor josgarithmetic made an error on the last step. It should be 6*(0.06-0.04)/(0.1-0.06)
The "1" should be "0.1" instead
That expression evaluates to 3.
I think it's beneficial to simplify along the way to avoid a sea of numbers.
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Here's how I would solve the problem.
x = amount of the 10% solution in liters
We have 6 liters of the 4% solution.
That contributes 0.04*6 = 0.24 liters of pure silver so far.
We add x liters of the 10% solution.
So we add 0.1x liters of pure silver to get 0.24+0.1x liters of pure silver total.
This is out of 6+x liters of solution of silver and other elements.
(amount of pure silver)/(amount of solution) = 6% goal
(0.24+0.1x)/(6+x) = 0.06
0.24+0.1x = 0.06(6+x)
0.24+0.1x = 0.36+0.06x
0.1x-0.06x = 0.36-0.24
0.04x = 0.12
x = 0.12/0.04
x = 3
Answer: 3 liters
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