Question

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 containing
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 create a 6 ounce liquid containing 8% reactor fuel, Mrs. Gargantua needs to use approximately 1.5 ounces of the 4% liquid solution.

Step-by-step explanation:

To solve this problem, we can use the formula for mixing solutions:

(percentage of solution A * quantity of solution A) + (percentage of solution B * quantity of solution B) = (percentage of final solution * quantity of final solution)

Let x be the quantity of the 4% liquid solution Mrs. Gargantua needs to use. Since the final solution is 6 ounces, the quantity of the 20% liquid solution is 6 - x ounces.

Plugging the values into the formula:

(4% * x) + (20% * (6 - x)) = 8% * 6

Solving this equation, we find that x is approximately 1.5 ounces. Therefore, Mrs. Gargantua needs to use 1.5 ounces of the 4% liquid solution.

Answer 2

She should used 4.5 ounces of the 4% and 1.5 ounces of the 20%.

Step-by-step explanation:

x = amount of 4% fuel

6 - x = amount of 20% fuel

0.04x + 0.2(6 - x) = 0.08(6) Multiply both sides by 100 to remove the decimals

4x + 20(6 - x) = 8(6)

4x + 120 - 20x = 48

-16x + 120 = 48

-16x = -72

x = 4.5

She should used 4.5 ounces of the 4% and 1.5 ounces of the 20%.