Meg has a solution that is 40% alcohol and another solution that is 60% alcohol. If Meg wants 12 gal of a solution that is 45% alcohol, how much of the two solutions must be mixed?
To determine the amount of each solution Meg needs to mix, we can use a basic algebraic equation.
Let's assume Meg needs to mix x gallons of the 40% alcohol solution and (12 - x) gallons of the 60% alcohol solution to get a 45% alcohol solution.
Now, let's set up the equation:
0.40x + 0.60(12 - x) = 0.45(12)
Explanation for the equation:
The left side of the equation represents the total amount of alcohol in the mixture. For the 40% solution, 0.40x represents the amount of alcohol in x gallons, and for the 60% solution, 0.60(12 - x) represents the amount of alcohol in (12 - x) gallons.
The right side of the equation represents the desired amount of alcohol in the 45% solution. 0.45(12) represents the amount of alcohol in 12 gallons of the 45% solution.
Now, let's solve the equation:
0.40x + 0.60(12 - x) = 0.45(12)
0.40x + 7.2 - 0.60x = 5.4
-0.20x + 7.2 = 5.4
-0.20x = 5.4 - 7.2
-0.20x = -1.8
x = (-1.8) / (-0.20)
x = 9
Therefore, Meg needs to mix 9 gallons of the 40% alcohol solution and (12 - 9) = 3 gallons of the 60% alcohol solution to obtain a 12-gallon solution that is 45% alcohol.
if she uses x gallons of 40%, then
.40x + .60(12-x) = .45(12)
The answer I got was 9 gal of the 40% alcohol solution and 3 gal of the 60% alcohol solution is needed. Am I right?
Julie bought a card good for 35 visits to a health club and began a workout routine. After y visits, she had y fewer than 35 visits remaining on her card. After 18 visits, how many visits did she have left?
McKenna, you are right.
note that 45% is 1/4 of the way from 40 to 60, so only 1/4 of the total is the higher concentration.
Just sayin' . . .
As for Julie, she had 35-18=17 visits left