Answer:
20 gallons of 15% solution must be mixed with 5 gallons of 40% solution.
Step-by-step explanation:
40% of 5 gallons is 2 gallons of sugar
x represents the number of gallons of solution to be added.
15% of x is sugar.
The total amount of sugar must be equal to 20% of the final mixture.
The end mixture will be x + 5 gallons
Change percent to decimal for the equation:
.2(x +5) = .15x +2
.2x +1 = .15x +2
.2x - .15x = 2 -1
.05x = 1
x = 20
Check:
.2(20 +5) = .15(20) +2
.2(25) = 3 + 2
5 = 5 true
This means that adding 20 gallons of the 15% solution is adding 3 gallons of sugar [along with 17 gallons of water] to the 2 gallons of sugar in the original mixture.
20% of the 25 gallons, 5 gallons, of the final mixture is sugar. 80% [ 3+17 = 20 gallons] is water.
