Question

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?

Answer 1

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.