Question 1201492
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Answer: <font color=red size=4>3 liters of water</font>



Explanation:


x = amount of liters of pure water to add
this is some positive real number


I'll draw out a mixture table.
The table is optional but it might help clear up confusion, and also keep things organized.
<table border = "1" cellpadding = "5"><tr><td></td><td>Water</td><td>Weed Killer</td><td>Total</td></tr><tr><td>start</td><td>4.6</td><td>0.4</td><td>5</td></tr><tr><td>add</td><td>x</td><td>0</td><td>x</td></tr><tr><td>end</td><td>4.6+x</td><td>0.4</td><td>5+x</td></tr></table>
The first row of the table is "start" to represent what we have at first: the 8% solution.


8% of 5 = 0.08*5 = 0.4 liters of pure weed killer
5-0.4 = 4.6 liters of water


The second row is labeled "add" to represent the next mixture. In this case it's pure water. 
It's just water and nothing else.
We have x liters of this and 0 liters of weed killer.


The "water" column adds to 4.6+x. Simply add straight down.
The "weed killer" column adds to 0.4+0 = 0.4
The totals add to 5+x


The final mix will have 0.4 liters of pure weed killer out of 5+x liters total solution (water+weed killer)


The ratio of these items must be 5% because want a 5% solution.


A = amount of pure weed killer = 0.4
B = total amount of solution = 5+x
A/B = 5% solution
A/B = 0.05
(0.4)/(5+x) = 0.05
0.4 = 0.05*(5+x)
0.4 = 0.25+0.05x
0.4-0.25 = 0.05x
0.15 = 0.05x
0.05x = 0.15
x = 0.15/0.05
x = <font color=red>3</font>
We need to add <font color=red>3 liters</font> of pure water to achieve a 5% solution.
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