Pewee adds two liters of pure alcohol to a 30% solution of alcohol in water. If the new concentration is 40%, how many liters of the original solution were there?
.3 x + 2 = .4(2+x)
Well, well, well! Looks like Pewee had a little "spirited" adventure with those alcohols! Let's do some math, shall we?
Let's assume that the number of liters in the original solution was x. Now, if Pewee added 2 liters of pure alcohol, we'll have (x + 2) liters of the new solution.
According to the problem, the new concentration is 40%. This means that the amount of alcohol in the new solution is 40% of (x + 2) liters.
Now, let's set up an equation to solve this booze puzzle:
0.3x + 2 = 0.4(x + 2)
Let's simplify:
0.3x + 2 = 0.4x + 0.8
Subtract 0.3x from both sides:
2 = 0.1x + 0.8
Subtract 0.8 from both sides:
1.2 = 0.1x
Divide both sides by 0.1:
x = 12
VoilĂ ! Looks like there were 12 liters of the original solution. Pewee sure knows how to mix things up! *honk honk*
To solve this problem, we can set up an equation based on the given information.
Let's assume that the original solution has a volume of x liters.
In the original solution, since it is a 30% alcohol solution, this means that 30% of x liters is pure alcohol. So, we have 0.30x liters of pure alcohol in the original solution.
When Pewee adds 2 liters of pure alcohol to the solution, the total amount of pure alcohol becomes 0.30x + 2 liters.
The new concentration is said to be 40%. This means that 40% of the total volume is pure alcohol.
Setting up the equation:
0.40(x + 2) = 0.30x + 2
Now, we can solve the equation for x, which represents the original volume of the solution.
0.40x + 0.80 = 0.30x + 2
0.40x - 0.30x = 2 - 0.80
0.10x = 1.20
x = 1.20 / 0.10
x = 12
Therefore, the original solution had a volume of 12 liters.
To solve this problem, we can use the concept of mixing two different solutions together. Let's break down the information given:
1) Pewee adds two liters of pure alcohol to a 30% solution of alcohol in water.
2) The new concentration after mixing is 40%.
The first step is to determine the initial amount of alcohol in the 30% solution. Let's assume there were "x" liters of the 30% solution. As the concentration is given in terms of the percentage of alcohol, we can write:
0.30 * x = amount of alcohol in the 30% solution
The amount of pure alcohol (100% concentration) that is added is 2 liters. Therefore, the total amount of alcohol after mixing is given by:
amount of alcohol in the 30% solution + amount of pure alcohol added = total amount of alcohol after mixing
0.30 * x + 2 = amount of alcohol after mixing
Since the new concentration after mixing is 40%, we can write:
0.40 * (x + 2) = amount of alcohol after mixing
Now, we can set these two expressions equal to each other and solve for "x", the initial amount of the 30% solution:
0.30 * x + 2 = 0.40 * (x + 2)
Now, let's solve this equation:
0.30 * x + 2 = 0.40 * x + 0.40 * 2
0.30 * x + 2 = 0.40 * x + 0.80
0.30 * x - 0.40 * x = 0.80 - 2
-0.10 * x = -1.20
x = -1.20 / -0.10
x = 12
Therefore, there were 12 liters of the original 30% alcohol solution.