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

5 dozen

12 dozen

13 3/4
dozen

Answer 1

To find out how many beads Yolanda has left in the box, we need to perform the following steps:

1. Calculate the total number of beads Yolanda has initially.
2. Calculate the total number of beads she used for the necklace and bracelet.
3. Subtract the total used from the initial amount.

### Step 1: Total initial beads
Yolanda has 8 3/4 dozen beads. To convert that into an improper fraction:
\[
8 \frac{3}{4} = \frac{8 \times 4 + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4} \text{ dozen}
\]

### Step 2: Total beads used
Yolanda used:
- 3 1/4 dozen for the necklace:
\[
3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4} \text{ dozen}
\]
- 1 3/4 dozen for the bracelet:
\[
1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4} \text{ dozen}
\]

Now, add the beads used:
\[
\frac{13}{4} + \frac{7}{4} = \frac{20}{4} = 5 \text{ dozen}
\]

### Step 3: Remaining beads
Now, we subtract the total beads used from the initial beads:
\[
8 \frac{3}{4} - 5 = 3 \frac{3}{4} \text{ dozen}
\]

Thus, the amount of beads left in the box is:
\[
\text{Answer: } 3 \frac{3}{4} \text{ dozen}
\]