# 4Tests Forums

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 Author Topic da1tigers Posted - 26 March 2013 11:5  A paint company mixes it's paint with water to create more paint per gallon. They currently have ten gallon jugs which contain 10% water. How much water must they add to create a 80/20 mix of paint to water?the answer is 1.25 but I dont understand how they got it and it is not explained well when u check the answer lema38 Posted - 29 March 2013 15:2  (10+x)/(1+x)=(80+20)/20
x=1.25 FredGee Posted - 29 March 2013 21:50  imagine the buckets

10 buckets (a gallon each) that are 10% water and 90% paint

they want it to be 20% water and 80% paint

you can see straight away that you start with 1 gallon of water and 9 gallons of paint

the simple intuitive thing is to think that adding another gallon of water will make it 20% water and 80% paint

but not so - you end up with 2 gallons of water but there is still only 9 gallons of paint

so 2 gallons of water out of a total of 11 gallons (of paint and water) is a mix with only 18.18% water

2 gallons of water in 10 gallons of paint and water would be 20% but we have 11 gallons of total mix (because we added the water) - so more water needed

if you think 'Z' is the amount of water you need to put in to bring the whole mix to 20% water, then all you need is a simple equation where the one gallon of water (already in the mix) plus 'Z' will make the total mix 20% water (you need to think about how adding something to the total changes the total)

so (1+Z) divided by (10+Z) should equal 0.2 (or 20%)

we know we start with 1 gallon of water and 10 gallons of total mix (water and paint) - so we need to find how much more water to add using an equation that takes account of how much water we add and how the amount of the total mix is affected (to get the required proportion)

can you see that the same 'Z' is in the water that you are adding to the mix and in the total mix

(1+Z)/(10+Z) = 0.2 (or a fifth)

than you can see straight away from the given answers that

1 gallon (1+1)/(10+1) = 2/11 is not 0.2 wrong!
1.25 gallons (1+1.25)/(10+1.25) = 2.25/11.25 is 0.2 (or a filth, 5x2 is 10 and 5x0.25 = 1.25)
1.5 gallons wrong!
1.75 gallons wrong!
2 gallons wrong!

Don't worry - almost everybody finds these types of question difficult to get their head round at the start but after a getting a few right - easy peasey

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