2. Arlene makes a necklace using 14 purple beads for every 6 silver beads. The neckla contains 80 beads. How many of each col bead are in the necklace?

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UpStudy AI · Accepted Answer

To determine the number of purple and silver beads in Arlene's necklace, let's break down the problem step by step.

**Given:**
- **Ratio of Purple to Silver Beads:** 14:6
- **Total Beads in Necklace:** 80

**Step 1: Simplify the Ratio**
The ratio of purple to silver beads can be simplified by dividing both numbers by their greatest common divisor, which is 2.

$$
\frac{14}{2} : \frac{6}{2} = 7:3
$$

So, the simplified ratio is **7:3**.

**Step 2: Express the Number of Beads in Terms of a Variable**
Let’s denote the common multiplier as $$ x $$.

- **Number of Purple Beads:** $$ 7x $$
- **Number of Silver Beads:** $$ 3x $$

**Step 3: Set Up the Equation Based on the Total Number of Beads**
$$
7x + 3x = 80
$$
$$
10x = 80
$$
$$
x = 8
$$

**Step 4: Calculate the Number of Each Type of Bead**
- **Purple Beads:** $$ 7x = 7 \times 8 = 56 $$
- **Silver Beads:** $$ 3x = 3 \times 8 = 24 $$

**Conclusion:**
Arlene's necklace contains **56 purple beads** and **24 silver beads**.

---

**Answer:**  
56 purple beads and 24 silver beads are in the necklace.
Arlene's necklace has 56 purple beads and 24 silver beads.

2. Arlene makes a necklace using 14 purple beads for every 6 silver beads. The neckla contains 80 beads. How many of each col bead are in the necklace?

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