mrs. gargantua thinks she finally may have found a medicine which will remove the blackness from her teeth. But first she has to mix a liquid containing 4% reactor fuel with a liquid contain 20% reactor fuel to create a 6 ounce liquid containing 8% reactor fuel. How many ounces of the 4% liquid must she use? Round your answer to the nearest one decimal place (tenths).

Answer 1

To solve this problem, we can use a system of equations based on the information given.

Let's denote:

• \( x \) = the amount of the 4% liquid (in ounces)
• \( y \) = the amount of the 20% liquid (in ounces)

From the problem, we know that:

1. The total volume of the mixture is 6 ounces: \[ x + y = 6 \]

2. The total amount of reactor fuel in the final mixture should equal 8% of 6 ounces: \[ 0.04x + 0.20y = 0.08 \times 6 \] Simplifying the right side gives: \[ 0.04x + 0.20y = 0.48 \]

Now we have a system of equations:

1. \( x + y = 6 \)
2. \( 0.04x + 0.20y = 0.48 \)

We can solve for \( y \) from the first equation: \[ y = 6 - x \]

Substituting \( y \) into the second equation gives: \[ 0.04x + 0.20(6 - x) = 0.48 \] Expanding this: \[ 0.04x + 1.2 - 0.20x = 0.48 \] Combining like terms: \[ -0.16x + 1.2 = 0.48 \] Now, isolate \( x \): \[ -0.16x = 0.48 - 1.2 \] \[ -0.16x = -0.72 \] Dividing both sides by -0.16: \[ x = \frac{-0.72}{-0.16} = 4.5 \]

Now that we have \( x \), we can find \( y \): \[ y = 6 - x = 6 - 4.5 = 1.5 \]

Thus, the amount of the 4% liquid that Mrs. Gargantua must use is: \[ \boxed{4.5 \text{ ounces}} \]