A barrel contained 10 gallons of water and 2 gallons of oil. How many gallons of a solution that is 5% oil and 95% water must be added to the barrel to dilute the oil down to 10% of the total volume in the barrel?

Question

paxpolaris · Answer

oil and water don't mix

anonymous · Answer

lol. I'm terrible at these kinds of problems for some reason...can you guide me through it?

paxpolaris · Answer

if you are adding x gallons of solution:$$\Large {2+0.05x \over 12+x} = 10\%$$

anonymous · Answer

? I don't really get what that means

paxpolaris · Answer

after adding x gallons of the 5% oil solution:
total volume = x plus the 12 gallons already in barrel

volume of oil= 2gallons alreasy in barrel + 5% of x added

paxpolaris · Answer

after adding solution $$\Large {\text{volume of oil} \over \text{total volume}} =10\% \ \ or\ \frac1{10}$$

anonymous · Answer

x + 12 = y
0.05x + 2 = 0.1y

0.05x + 2 = 0.1(x + 12)
0.05x + 2 = 0.1x + 1.2
0.05x = 0.8
x = 16
Did I do it correctly?

paxpolaris · Answer

never mind it 's correct

anonymous · Answer

Alright. Thanks! I can never seem to do these problems. Is there a different way that you would do it or is that the way you're supposed to do it?

paxpolaris · Answer

all ways are pretty similar....

anonymous · Answer

Oh alright THanks :)