How many gallons of a 15% sugar solution must be mixed with a 5 gallons of a 40% solution to make a 20% solution

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.

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step-by-step explanation: