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.
-
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: \[ 8 \frac{3}{4} = \frac{8 \times 4 + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4} \text{ dozen} \]
-
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: \[ 1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4} \text{ dozen} \]
-
Add the beads used: \[ \text{Total used} = \frac{13}{4} + \frac{7}{4} = \frac{13 + 7}{4} = \frac{20}{4} = 5 \text{ dozen} \]
-
Subtract the total used from the initial quantity: \[ \text{Beads left} = \frac{35}{4} - \frac{20}{4} = \frac{35 - 20}{4} = \frac{15}{4} \text{ dozen} \]
-
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.