SOLUTION: A tank contain water and oil in the ratio 5 :3. If 16 gallen mixture is taken out from this mixture and 16 gallen oil is added to it then ratio of water and oil becomes 3 :5. How m

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A tank contain water and oil in the ratio 5 :3. If 16 gallen mixture is taken out from this mixture and 16 gallen oil is added to it then ratio of water and oil becomes 3 :5. How m      Log On


   

Question 980892: A tank contain water and oil in the ratio 5 :3. If 16 gallen mixture is taken out from this mixture and 16 gallen oil is added to it then ratio of water and oil becomes 3 :5. How many gallen of mixture are there in the original mixture.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A tank contain water and oil in the ratio 5:3.
If gallons of the mixture is taken out from this mixture and 16 gallons of oil is added to it, then ratio of water and oil becomes 3:5.
How many gallons of mixture are there in the original mixture.
:
let x = amt of the mixture
:
a mixture of 5:3 would have a fractional amt of oil of 3%2F8x
a mixture of 3:5 would have a fractional amt of oil of 5%2F8x
:
An equation based on the amt of oil
3%2F8(x-16) + 16 = 5%2F8x
multiply by 8 to get rid of the denominators, resulting in:
3(x-16) + 8(16) = 5x
3x - 48 + 128 = 5x
3x + 80 = 5x
80 = 5x - 3x
80 = 2x
x = 80/2
x = 40 gallons in the mixture:
:
Check
3%2F8(40-16) + 16 = 5%2F8(40)
3%2F8(24) + 16 = 5%2F8(40)
do the math
9 + 16 = 25