Question 1201492: How much water must be added to 5L of 8% weed killer mixture to make a 5% weed killer mixture? Found 2 solutions by math_tutor2020, greenestamps:Answer by math_tutor2020(3817) (Show Source):
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.
Water
Weed Killer
Total
start
4.6
0.4
5
add
x
0
x
end
4.6+x
0.4
5+x
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 = 3
We need to add 3 liters of pure water to achieve a 5% solution.
A description of the standard setup for solving the problem using formal algebra:
You are mixing 5 liters that is 8% weed killer to an unknown number of liters x that is 0% weed killer, resulting in (5+x) liters that is 5% weed killer:
ANSWER: 3 liters
If formal algebra is not required, here is a fast and easy informal way to solve the problem.
You are mixing 0% weed killer and 8% weed killer to get 5% weed killer.
5% is 5/8 of the way from 0% to 8%. (Picture the three percentages on a number line, if it helps.)
That means 5/8 of the mixture is the 8% weed killer.
So 5/8 of the mixture is the 5 liters of 8% weed killer that you started with; that means 3/8 of the mixture is the water you added.
Since 5/8 of the mixture is 5 liters, 3/8 of the mixture is 3 liters.
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