Equation by substitution

Question

5.) A 50 gallon barrel (full) contains an unknown alcohol solution from the 17 hundreds. Per the old incomplete records this solution was achieved by mixing 30 gallons of a 100% solution with a 75% solution. What is the % of the unknown solution and how many gallons of 75% solution were used.

Answer 1

50-30 = 20 = the number of gallons of the 75% solution

30 of 50 or 3/5 is 100% solution. the remaining 20 of 50 or 2/5 is 75% solution

3/5(1.00) + .75(2/5) = ,60 + .30 = .90 =90% solution of 50 gallons

Add 20 gallons of 75% solution to 30 gallons of 100% solution to get 50 gallons of 90% solution