claude ebair hs hired a team of chemists to create the worlds longest lasting perfume, which he plans to call 24/7. On their first attempt, the chemist combined 5 milliliters of a substance containing 2% sandalwood with another substance containing 6% sandalwood to get a substance containing 5% sandalwood. How many milliliters of the substance containing 6% sandalwood must the chemists have used?

Question

GPT-4o mini · Answer

Let $ x $ be the number of milliliters of the substance containing 6% sandalwood. The chemists combined 5 milliliters of the substance containing 2% sandalwood with $ x $ milliliters of the substance containing 6% sandalwood. The total volume of the new mixture is: $$ 5 + x $$ Next, we need to calculate the amount of sandalwood in each substance: - The amount of sandalwood from the 5 milliliters of the 2% substance is: $$ 0.02 \times 5 = 0.1 \text{ milliliters} $$ - The amount of sandalwood from $ x $ milliliters of the 6% substance is: $$ 0.06x \text{ milliliters} $$ The total amount of sandalwood in the final mixture, which is 5% of the total volume, can be expressed as: $$ 0.05(5 + x) $$ Now we can set up the equation for the total amount of sandalwood in the mixture: $$ 0.1 + 0.06x = 0.05(5 + x) $$ Next, we'll simplify the right side of the equation: $$ 0.1 + 0.06x = 0.25 + 0.05x $$ Now we'll rearrange the equation to isolate $ x $: $$ 0.06x - 0.05x = 0.25 - 0.1 $$ This simplifies to: $$ 0.01x = 0.15 $$ Now, dividing both sides by 0.01 gives: $$ x = \frac{0.15}{0.01} = 15 $$ Thus, the chemists must have used **15 milliliters** of the substance containing 6% sandalwood.