Answer:
Explanation:
To determine how much of Brand A fruit punch (30% fruit juice) must be mixed with 3 gallons of Brand B fruit punch (50% fruit juice) to create a mixture containing 35% fruit juice, we can use a proportion.
Let's start by setting up the equation. We'll use "x" to represent the amount of Brand A fruit punch needed.
The total volume of the mixture will be 3 gallons + x gallons.
The equation can be set up as follows:
0.30x + 0.50(3) = 0.35(3 + x)
Simplifying the equation:
0.30x + 1.5 = 1.05 + 0.35x
Next, we can subtract 0.35x from both sides of the equation to isolate the "x" term:
0.30x - 0.35x + 1.5 = 1.05
0.05x + 1.5 = 1.05
Subtract 1.5 from both sides:
0.05x = 1.05 - 1.5
0.05x = -0.45
Finally, divide both sides of the equation by 0.05 to solve for "x":
x = -0.45 / 0.05
x = -9
The solution "x = -9" doesn't make sense in this context, as we can't have a negative volume.
Therefore, there seems to be an error in the problem or the equation setup. Please double-check the information provided or consult with your teacher to clarify the problem statement.