Question

a company makes first - aid kits in different sizes. the ratio of fabric bandages to plastic bandages in each kit is 3 to 9. a small kit has 16 fabric bandages. how many plastic bandages does a small kit have? show your work.

Explanation:

Step1: Simplify the ratio

The ratio of fabric bandages to plastic bandages is \( 3:9 \), which simplifies to \( 1:3 \) (dividing both parts by 3). This means for every 1 fabric bandage, there are 3 plastic bandages.

Step2: Set up a proportion

Let \( x \) be the number of plastic bandages. We know that the ratio of fabric to plastic is \( 1:3 \), and we have 16 fabric bandages. So we set up the proportion:
\( \frac{1}{3}=\frac{16}{x} \)

Step3: Solve for \( x \)

Cross - multiply: \( 1\times x = 3\times16 \)
\( x = 48 \)

Answer:

A small kit has 48 plastic bandages.