Nadine mixes a juice solution that is made from 3 gallons of an 80% juice solution and 1 gallon of a 20% juice solution. what is the percent concentration of the final solution? 25% 50% 65% 70%

The rule that we will use to solve this question is:
M1V1 + M2V2 = M3V3
where:
M1 is the concentration of the first solution = 80% = 0.8
V1 is the volume of the first solution = 3 gallons
M2 is the concentration of the second solution = 20% = 0.2
V2 is the volume of the second solution = 1 gallon
M3 in the final concentration that we want to calculate
V3 is the final volume = 3 gallons + 1 gallon = 4 gallons

Substitute with the givens in the above equation to get the final concentration as follows:
M1V1 + M2V2 = M3V3
(0.8)(3) + (0.2)(1) = (4)M3
2.4 + 0.2 = 4M3
2.6 = 4M3
M3 = 2.6/4
M3 = 0.65

To get the percentage, we will multiply the concentration by 100 as follows:
% of concentration = 0.65 * 100 = 65%