Question

1. you use \\(\frac{1}{32}\\) milliliter of essential oils for every \\(\frac{3}{4}\\) milliliter of avocado oil to make 150 milliliters of a solution.\

a. how much essential oils do you use? how much avocado oil do you use?\
b. you decide that you want to add coconut oil to the solution. you make the new mixture by adding \\(\frac{3}{16}\\) milliliter of coconut oil for every \\(\frac{1}{32}\\) milliliter of essential oils and \\(\frac{3}{4}\\) milliliter of avocado oil. how much essential oils, avocado oil, and coconut oil do you use to make \\(15\frac{1}{2}\\) milliliters of the new solution?\

1. the ratio of white rice to water is 1 to \\(2\frac{1}{2}\\). you have \\(\frac{2}{3}\\) cup of rice. how much water do you need?

Explanation:

Step1: Find oil ratio (part a)

Ratio of essential oil to avocado oil: $\frac{1}{32} : \frac{3}{4} = 1:24$
Total parts = $1+24=25$

Step2: Calculate essential oil (part a)

Volume of essential oil: $\frac{1}{25} \times 150 = 6$ milliliters

Step3: Calculate avocado oil (part a)

Volume of avocado oil: $\frac{24}{25} \times 150 = 144$ milliliters

Step4: Find new ratio (part b)

Ratio: $\frac{1}{32} : \frac{3}{4} : \frac{3}{16} = 1:24:6$
Total parts = $1+24+6=31$
Convert $15\frac{1}{2}$ to $\frac{31}{2}$ milliliters

Step5: Calculate each oil (part b)

Essential oil: $\frac{1}{31} \times \frac{31}{2} = \frac{1}{2}$ milliliters
Avocado oil: $\frac{24}{31} \times \frac{31}{2} = 12$ milliliters
Coconut oil: $\frac{6}{31} \times \frac{31}{2} = 3$ milliliters

Step6: Calculate water (problem 9)

Ratio of rice to water: $1:2\frac{1}{2}=1:\frac{5}{2}$
Water needed: $\frac{2}{3} \times \frac{5}{2} = \frac{5}{3}$ cups

Answer:

Part 8a:

• Essential oil: 6 milliliters
• Avocado oil: 144 milliliters

Part 8b:

• Essential oil: $\frac{1}{2}$ milliliter
• Avocado oil: 12 milliliters
• Coconut oil: 3 milliliters

Problem 9:

• Water needed: $\frac{5}{3}$ cups (or $1\frac{2}{3}$ cups)