SOLUTION: How many gallons of water must be added to 40 gallons of 10% alcohol solution to produce a 8% alcohol solution? What would be the formula to this type of problem?

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Question 714695: How many gallons of water must be added to 40 gallons of 10% alcohol solution to produce a 8% alcohol solution? What would be the formula to this type of problem?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You ask, what would be the formula! Very good question. Let's solve the problem purely symbolically!

P = current percentage concentration of alcohol, 10%
T = target percentage that we want, 8%
M = volume of solution or mixture currently, 40 gallons
w = how many gallons of water to add (volume) to reach T; UNKNOWN

ONE equation to relate the percentages used in the description of the problem:
(Amount of Alcohol)/(Amount of Solution)=(Percent Alcohol)

highlight%28M%2AP%2F%28M%2Bw%29=T%29, Our fundamental equation. We will keep the next few steps in symbols, variables only.

MP=T%28M%2Bw%29
MP=TM%2BTw
TM%2BTw=MP
Tw=MP-TM
w=%28MP-MT%29%2FT, a reasonable form already
highlight%28w=M%28P-T%29%2FT%29, Our fundamental formula for how much water to add, as gallons volume