Question

Arianna is selling necklaces and bracelets at a local craft fair. She buys 8 yards of string. She uses 1 1/2 yards to make necklaces and the rest to make bracelets requires 3/4 yards of string. How many bracelets can she make?

Answer 1

To determine how many bracelets Arianna can make, we first need to find out how much string she has left after making the necklaces.

1. **Calculate the string used for necklaces**:
\[
\text{String used for necklaces} = 1 \frac{1}{2} \text{ yards} = \frac{3}{2} \text{ yards}
\]

2. **Determine the remaining string**:
\[
\text{Total string} = 8 \text{ yards}
\]
\[
\text{String remaining} = \text{Total string} - \text{String used for necklaces}
\]
\[
\text{String remaining} = 8 - \frac{3}{2}
\]

To subtract these, we can convert 8 into a fraction:
\[
8 = \frac{16}{2}
\]
Now perform the subtraction:
\[
\text{String remaining} = \frac{16}{2} - \frac{3}{2} = \frac{16 - 3}{2} = \frac{13}{2} \text{ yards}
\]

3. **Calculate how many bracelets can be made**:
Each bracelet requires \(\frac{3}{4}\) yards of string. To find out how many bracelets Arianna can make, we divide the remaining string by the amount needed for each bracelet:
\[
\text{Number of bracelets} = \frac{\text{String remaining}}{\text{String per bracelet}} = \frac{\frac{13}{2}}{\frac{3}{4}}
\]

To divide fractions, multiply by the reciprocal:
\[
\text{Number of bracelets} = \frac{13}{2} \times \frac{4}{3}
\]
\[
= \frac{13 \times 4}{2 \times 3} = \frac{52}{6} = \frac{26}{3}
\]

Evaluating \(\frac{26}{3}\) gives us approximately 8.67. Since Arianna cannot make a fraction of a bracelet, we round down to the nearest whole number.

Therefore, the maximum number of bracelets Arianna can make is:
\[
\boxed{8}
\]