Question
Aaliyah wants to have 8 pounds of candy for her party. She has 2 1/3 pounds of Swedish fish, 1 3/4 pounds of sour patch kids, and 3 1/2 pounds of chocolate. Does Aaliyah have at least 8 pounds of candy? If she doesn’t have at least 8 pounds of candy, how many more pounds of candy does she need?
Answer:
Answer:
Answers
GPT-4o mini
To determine if Aaliyah has at least 8 pounds of candy, we need to add together the amounts of the three types of candy she has:
1. **Swedish fish:** \( 2 \frac{1}{3} \) pounds
2. **Sour patch kids:** \( 1 \frac{3}{4} \) pounds
3. **Chocolate:** \( 3 \frac{1}{2} \) pounds
First, let's convert these mixed numbers into improper fractions:
1. \( 2 \frac{1}{3} = \frac{7}{3} \) (because \( 2 \times 3 + 1 = 7 \))
2. \( 1 \frac{3}{4} = \frac{7}{4} \) (because \( 1 \times 4 + 3 = 7 \))
3. \( 3 \frac{1}{2} = \frac{7}{2} \) (because \( 3 \times 2 + 1 = 7 \))
Next, we need a common denominator to add these fractions. The least common multiple of 3, 4, and 2 is 12.
Now, we convert each fraction to have a denominator of 12:
1. \( \frac{7}{3} = \frac{7 \times 4}{3 \times 4} = \frac{28}{12} \)
2. \( \frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12} \)
3. \( \frac{7}{2} = \frac{7 \times 6}{2 \times 6} = \frac{42}{12} \)
Now, we can add these fractions:
\[
\frac{28}{12} + \frac{21}{12} + \frac{42}{12} = \frac{28 + 21 + 42}{12} = \frac{91}{12}
\]
Now, we convert the improper fraction \( \frac{91}{12} \) back to a mixed number:
To find the whole number, we divide 91 by 12:
- \( 91 ÷ 12 = 7 \) remainder \( 7 \) (because \( 12 \times 7 = 84\))
Thus, \( \frac{91}{12} = 7 \frac{7}{12} \).
Now we compare this with 8 pounds:
Aaliyah has \( 7 \frac{7}{12} \) pounds of candy. To find out how much more she needs to reach 8 pounds:
1. Convert 8 pounds to a fraction (as an improper fraction):
- \( 8 = \frac{96}{12} \)
2. Find the difference:
\[
\frac{96}{12} - \frac{91}{12} = \frac{5}{12}
\]
Hence, Aaliyah needs \( \frac{5}{12} \) more pounds of candy to reach the 8 pounds she wants.
**Answer:** No, Aaliyah does not have at least 8 pounds of candy. She needs \( \frac{5}{12} \) more pounds of candy.
1. **Swedish fish:** \( 2 \frac{1}{3} \) pounds
2. **Sour patch kids:** \( 1 \frac{3}{4} \) pounds
3. **Chocolate:** \( 3 \frac{1}{2} \) pounds
First, let's convert these mixed numbers into improper fractions:
1. \( 2 \frac{1}{3} = \frac{7}{3} \) (because \( 2 \times 3 + 1 = 7 \))
2. \( 1 \frac{3}{4} = \frac{7}{4} \) (because \( 1 \times 4 + 3 = 7 \))
3. \( 3 \frac{1}{2} = \frac{7}{2} \) (because \( 3 \times 2 + 1 = 7 \))
Next, we need a common denominator to add these fractions. The least common multiple of 3, 4, and 2 is 12.
Now, we convert each fraction to have a denominator of 12:
1. \( \frac{7}{3} = \frac{7 \times 4}{3 \times 4} = \frac{28}{12} \)
2. \( \frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12} \)
3. \( \frac{7}{2} = \frac{7 \times 6}{2 \times 6} = \frac{42}{12} \)
Now, we can add these fractions:
\[
\frac{28}{12} + \frac{21}{12} + \frac{42}{12} = \frac{28 + 21 + 42}{12} = \frac{91}{12}
\]
Now, we convert the improper fraction \( \frac{91}{12} \) back to a mixed number:
To find the whole number, we divide 91 by 12:
- \( 91 ÷ 12 = 7 \) remainder \( 7 \) (because \( 12 \times 7 = 84\))
Thus, \( \frac{91}{12} = 7 \frac{7}{12} \).
Now we compare this with 8 pounds:
Aaliyah has \( 7 \frac{7}{12} \) pounds of candy. To find out how much more she needs to reach 8 pounds:
1. Convert 8 pounds to a fraction (as an improper fraction):
- \( 8 = \frac{96}{12} \)
2. Find the difference:
\[
\frac{96}{12} - \frac{91}{12} = \frac{5}{12}
\]
Hence, Aaliyah needs \( \frac{5}{12} \) more pounds of candy to reach the 8 pounds she wants.
**Answer:** No, Aaliyah does not have at least 8 pounds of candy. She needs \( \frac{5}{12} \) more pounds of candy.