An organic makeup company uses lemon oil in its face soap. The diagram shows the number of drops used in the soap.

Question

Diagram of drops of lemon oil. An unknown number corresponds with 0.8 ounces of soap, and 10 drops correspond with 2 ounces of soap.

© 2018 StrongMind


Part A: Which equation describes the proportional relationship between l,
drops of lemon oil, and s,
amount of soap?

Part B: How many drops of lemon oil are needed for 0.8
ounces of soap?

Select two answers: one for Part A and one for Part B.

Responses

A: s=0.2l
A: s is equal to 0 point 2 l

B: 4
drops
B: 4 drops

A: s=0.8l
A: s is equal to 0 point 8 l

A: s=0.5l
A: s is equal to 0 point 5 l

B: 1.6
drops
B: 1 point 6 drops

B: 8
drops
B: 8 drops

A: s=2l
A: s is equal to 2 l

B: 2
drops
B: 2 drops

Answer 1

To solve the problem, we need to establish the relationship between the number of drops of lemon oil (l) and the amount of soap in ounces (s).

Part A: We know that:

• 10 drops correspond to 2 ounces of soap.

This can be expressed as: \[ \frac{10 \text{ drops}}{2 \text{ ounces}} = \frac{l}{s} \]

From this, we can find the ratio of drops to ounces: \[ 5 \text{ drops} = 1 \text{ ounce} \] Thus, the relationship can be expressed as: \[ s = \frac{1}{5}l \] or equivalently: \[ s = 0.2l \]

So, for Part A, the answer is: A: s = 0.2l

Part B: To find out how many drops of lemon oil are needed for 0.8 ounces of soap, we can use the equation we just derived: \[ s = 0.2l \]

We can substitute s with 0.8: \[ 0.8 = 0.2l \]

To isolate l, we divide both sides by 0.2: \[ l = \frac{0.8}{0.2} = 4 \text{ drops} \]

So, for Part B, the answer is: B: 4 drops

Putting this together, your selections are:

• Part A: A: s = 0.2l
• Part B: B: 4 drops