Question

Yolanda has a box that contains 8,3/4
dozen beads. She uses 3,1/4
dozen beads for a necklace and 1,3/4
dozen beads for a bracelet. How many beads are left in the box?

(1 point)
Responses

3,3/4
dozen

3 3 4 dozen

5
dozen

5 dozen

12
dozen

12 dozen

13,3/4
dozen

Answer 1

To find out how many beads Yolanda has left in the box, we start by determining the total number of beads she started with and how many she used.

1. **Convert the total number of beads in the box to a simple fraction:**
Yolanda has \(8 \frac{3}{4}\) dozen beads.
- Convert this to an improper fraction:
\[
8 \frac{3}{4} = \frac{8 \times 4 + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4} \text{ dozen}
\]

2. **Calculate the total number of beads used for the necklace and bracelet:**
- She uses \(3 \frac{1}{4}\) dozen beads for the necklace:
\[
3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4} \text{ dozen}
\]
- She uses \(1 \frac{3}{4}\) dozen beads for the bracelet:
\[
1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4} \text{ dozen}
\]

3. **Add the beads used:**
\[
\text{Total used} = \frac{13}{4} + \frac{7}{4} = \frac{13 + 7}{4} = \frac{20}{4} = 5 \text{ dozen}
\]

4. **Subtract the total used from the initial quantity:**
\[
\text{Beads left} = \frac{35}{4} - \frac{20}{4} = \frac{35 - 20}{4} = \frac{15}{4} \text{ dozen}
\]

5. **Convert \(\frac{15}{4}\) back to a mixed number:**
\[
\frac{15}{4} = 3 \frac{3}{4} \text{ dozen}
\]

Therefore, the number of beads left in the box is \(3 \frac{3}{4}\) dozen.

The answer from your options is:
**3,3/4 dozen**.