How much of a(n) 60% orange juice drink must be mixed with 8 gallons of a 30% orange juice drink to obtain a mixture that is 50% orange juice?
.6x + .3(8) = .5(x+8)
times 10
6x + 24 = 5x + 40
x = 16
.6 x + (.3 * 8) = .5 (8 + x)
To solve this problem, we can set up a equation based on the mixture of orange juice. Let's denote the amount of the 60% orange juice drink as x.
The equation can be set up as follows:
0.6x + 0.3(8) = 0.5(x + 8)
Now, let's solve for x:
0.6x + 2.4 = 0.5x + 4
0.6x - 0.5x = 4 - 2.4
0.1x = 1.6
x = 1.6 / 0.1
x = 16
Therefore, we need 16 gallons of the 60% orange juice drink to mix with 8 gallons of the 30% orange juice drink in order to obtain a mixture that is 50% orange juice.
To solve this problem, we need to determine how much of a 60% orange juice drink should be mixed with 8 gallons of a 30% orange juice drink.
Let's break down the problem into smaller steps:
Step 1: Determine the desired amount of the mixture
We want to end up with a mixture that is 50% orange juice. This means the total volume of the mixture will be the sum of the volumes of the two drinks. Let's call the desired amount of the mixture "x" gallons.
Step 2: Set up the equation
We can set up an equation based on the volume of orange juice in the two drinks:
Volume of orange juice in 60% orange juice drink + Volume of orange juice in 30% orange juice drink = Volume of orange juice in the mixture
To calculate the volume of orange juice in each drink, we multiply the volume of the drink by its percentage of orange juice (expressed as a decimal):
0.60x + 0.30(8) = 0.50x
Step 3: Solve the equation
Solving the equation will give us the value of x, which represents the desired amount of the mixture:
0.60x + 2.4 = 0.50x
0.60x - 0.50x = -2.4
0.10x = -2.4
x = -2.4 / 0.10
x = 24
Step 4: Interpret the result
We have found that the desired amount of the mixture is 24 gallons.
Therefore, to obtain a mixture that is 50% orange juice, you will need to mix 24 gallons of the 60% orange juice drink with 8 gallons of the 30% orange juice drink.