Hailey makes a necklace with 24 blue beads and 32 purple beads. She wants to make a bracelet that has the same ratio of blue beads to purple beads as the necklace. She plans to use 6 blue beads for the bracelet. How many purple beads should Hailey use

To maintain the same ratio of blue beads to purple beads in both the necklace and the bracelet, we first need to find the ratio of blue to purple beads in the necklace. Here's how we can calculate it:

### Step 1: Find the ratio in the necklace
- The number of blue beads in the necklace = 24
- The number of purple beads in the necklace = 32

So, the ratio of blue beads to purple beads in the necklace is:
\[
\frac{24}{32} = \frac{3}{4}
\]
Thus, the ratio of blue to purple beads in the necklace is \(3:4\).

### Step 2: Apply the same ratio to the bracelet
Hailey plans to use 6 blue beads for the bracelet. To maintain the \(3:4\) ratio, we set up the following proportion:

\[
\frac{3}{4} = \frac{6}{x}
\]
where \(x\) is the number of purple beads she should use for the bracelet.

### Step 3: Solve the proportion
We can solve for \(x\) by cross-multiplying:
\[
3x = 6 \times 4
\]
\[
3x = 24
\]
\[
x = \frac{24}{3} = 8
\]

### Conclusion:
Hailey should use **8 purple beads** for the bracelet to maintain the same ratio of blue to purple beads.

Would you like a detailed explanation of ratios, or do you have any questions?

Here are 5 related questions for further practice:
1. What if Hailey wants to use 9 blue beads? How many purple beads should she use?
2. How would the number of purple beads change if she used 12 blue beads?
3. If Hailey wants to make a second necklace with 36 blue beads, how many purple beads would be needed?
4. What is the total number of beads in the necklace and bracelet combined?
5. Can you find the ratio of purple to total beads in the necklace?

**Tip:** When working with ratios, always simplify them first, as it makes solving proportional problems easier!

Hailey makes a necklace with 24 blue beads and 32 purple beads. She wants to make a bracelet that has the same ratio of blue beads to purple beads as the necklace. She plans to use 6 blue beads for the bracelet. How many purple beads should Hailey use?

Learn how to solve a ratio problem where Hailey uses 24 blue and 32 purple beads to make a necklace. Discover how to calculate the number of purple beads needed for a bracelet with 6 blue beads to maintain the same ratio. Perfect for students in Grades 5-7.

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