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%
Accepted Solution
A:
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%