<h3>Answer: 1.25 gallons</h3>
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Explanation:
They currently have ten gallon jugs that contain 10% water, so this means 0.10*10 = 1 gallon of the jug is water and the other 10-1 = 9 gallons is paint. This is assuming the cans are just paint and water.
The ratio of paint to water is 90:10 which reduces to 9:1
Often it helps to reduce as much as possible, but it's actually more handy in this case to keep it at 90:10 so you can see the two parts add back up to 100%
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Let x be the amount of water we add. This amount is in gallons.
We start off with 1 gallon of water and it bumps up to 1+x gallons of water.
The overall amount of 10 gallons also bumps up to 10+x gallons.
We want a ratio of 80:20 this time, so we want 20 parts water and 80 parts paint. In other words, we want 20/(20+80) = 20/100 = 20% water
Divide (1+x) over (10+x) to get (1+x)/(10+x). This represents the fraction of water. We want this fraction to be equal to 0.20, which is the 20% water amount. It is also equal to 20/100.
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(1+x)/(10+x) = 20/100
100(1+x) = 20(10+x) ... cross multiply
100+100x = 200+20x ... distribute
100x-20x = 200-100
80x = 100
x = 100/80 ... divide both sides by 80
x = 1.25
You need to add 1.25 gallons of water
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If you add 1.25 gallons of water, then,
amount of water = 1+x = 1+1.25 = 2.25
amount of paint&water = 10+x = 10+1.25 = 11.25
So you'll have 2.25 gallons of water out of 11.25 gallons of water&paint mix
2.25/11.25 = 0.2 = 20% water
This confirms our answer.
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Extra info:
1.25 gallons = 1 gallon + 1/4 gallon
1.25 gallons = 1 gallon + 1 quart
This is because 1 gallon = 4 quarts, so 1 quart = 1/4 gallon.
* r^2