Question
Casey picked 6 pounds of pears. Karen picked 48 ounces of cherries. Jude picked 2 pounds of apples. They are going to make fruit pies. Fruit Pie Recipe Fruit Amount Cherries 8 oz Apples 8 oz Pears 12 oz Select all of the true statements below. (1 point) Responses Together, Karen and Jude picked the same weight of fruit as Casey picked. Together, Karen and Jude picked the same weight of fruit as Casey picked. Casey picked 2 times the weight of fruit that Karen picked. Casey picked 2 times the weight of fruit that Karen picked. There is enough fruit to make 6 pies. There is enough fruit to make 6 pies. If they make as many pies as possible, there will be 4 pounds of pears left over. If they make as many pies as possible, there will be 4 pounds of pears left over. To make 8 pies, they would need 1 more pound of cherries and 2 more pounds of apples.
Answers
GPT-4o mini
Let's break down the fruit picked by each person and compare the amounts to see which statements are true.
1. **Weight of fruit picked:**
- Casey picked 6 pounds of pears.
- Karen picked 48 ounces of cherries, which is equivalent to 3 pounds (1 pound = 16 ounces, so 48 ounces ÷ 16 = 3 pounds).
- Jude picked 2 pounds of apples.
Total fruit weight for each person:
- Casey: 6 pounds
- Karen: 3 pounds
- Jude: 2 pounds
Together, Karen and Jude picked: \(3 \text{ pounds (Karen)} + 2 \text{ pounds (Jude)} = 5 \text{ pounds}\).
2. **Statements analysis:**
- **Together, Karen and Jude picked the same weight of fruit as Casey picked.**
- False (5 pounds ≠ 6 pounds).
- **Casey picked 2 times the weight of fruit that Karen picked.**
- True (6 pounds = 2 × 3 pounds).
- **There is enough fruit to make 6 pies.**
- The total required for 6 pies:
- Cherries: \(6 \text{ pies} \times 8 \text{ oz/pie} = 48 \text{ oz}\) (exactly 48 oz, which Karen picked).
- Apples: \(6 \text{ pies} \times 8 \text{ oz/pie} = 48 \text{ oz}\) (48 oz = 3 pounds, which Jude picked).
- Pears: \(6 \text{ pies} \times 12 \text{ oz/pie} = 72 \text{ oz}\) (72 oz = 4.5 pounds, which Casey picked).
- Since they have enough cherries and apples but not enough pears, this statement is **False**.
- **If they make as many pies as possible, there will be 4 pounds of pears left over.**
- The maximum number of pies they can make is limited by the pears. They have 6 pounds of pears, and to make as many pies as possible:
- Total pears needed for pies: 12 oz per pie
- Total pears available: 6 pounds = 96 oz
- Maximum pies with 96 oz pears: \(96 \text{ oz} ÷ 12 \text{ oz/pie} = 8 \text{ pies}\).
- They would use all 6 pounds of pears, leaving **0 pounds** left, not 4 pounds. **False**.
- **To make 8 pies, they would need 1 more pound of cherries and 2 more pounds of apples.**
- Total needed for 8 pies:
- Cherries: \(8 \text{ pies} \times 8 \text{ oz/pie} = 64 \text{ oz}\) (which is 4 pounds).
- Apples: \(8 \text{ pies} \times 8 \text{ oz/pie} = 64 \text{ oz}\) (which is 4 pounds).
- They have 48 oz of cherries (3 pounds) and 32 oz of apples (2 pounds).
- To meet the cherry requirement: \(4 \text{ pounds} - 3 \text{ pounds} = 1 \text{ pound of cherries needed}\)
- To meet the apple requirement: \(4 \text{ pounds} - 2 \text{ pounds} = 2 \text{ pounds of apples needed}\)
- This statement is **True**.
**Final True Statements:**
- Casey picked 2 times the weight of fruit that Karen picked.
- To make 8 pies, they would need 1 more pound of cherries and 2 more pounds of apples.
1. **Weight of fruit picked:**
- Casey picked 6 pounds of pears.
- Karen picked 48 ounces of cherries, which is equivalent to 3 pounds (1 pound = 16 ounces, so 48 ounces ÷ 16 = 3 pounds).
- Jude picked 2 pounds of apples.
Total fruit weight for each person:
- Casey: 6 pounds
- Karen: 3 pounds
- Jude: 2 pounds
Together, Karen and Jude picked: \(3 \text{ pounds (Karen)} + 2 \text{ pounds (Jude)} = 5 \text{ pounds}\).
2. **Statements analysis:**
- **Together, Karen and Jude picked the same weight of fruit as Casey picked.**
- False (5 pounds ≠ 6 pounds).
- **Casey picked 2 times the weight of fruit that Karen picked.**
- True (6 pounds = 2 × 3 pounds).
- **There is enough fruit to make 6 pies.**
- The total required for 6 pies:
- Cherries: \(6 \text{ pies} \times 8 \text{ oz/pie} = 48 \text{ oz}\) (exactly 48 oz, which Karen picked).
- Apples: \(6 \text{ pies} \times 8 \text{ oz/pie} = 48 \text{ oz}\) (48 oz = 3 pounds, which Jude picked).
- Pears: \(6 \text{ pies} \times 12 \text{ oz/pie} = 72 \text{ oz}\) (72 oz = 4.5 pounds, which Casey picked).
- Since they have enough cherries and apples but not enough pears, this statement is **False**.
- **If they make as many pies as possible, there will be 4 pounds of pears left over.**
- The maximum number of pies they can make is limited by the pears. They have 6 pounds of pears, and to make as many pies as possible:
- Total pears needed for pies: 12 oz per pie
- Total pears available: 6 pounds = 96 oz
- Maximum pies with 96 oz pears: \(96 \text{ oz} ÷ 12 \text{ oz/pie} = 8 \text{ pies}\).
- They would use all 6 pounds of pears, leaving **0 pounds** left, not 4 pounds. **False**.
- **To make 8 pies, they would need 1 more pound of cherries and 2 more pounds of apples.**
- Total needed for 8 pies:
- Cherries: \(8 \text{ pies} \times 8 \text{ oz/pie} = 64 \text{ oz}\) (which is 4 pounds).
- Apples: \(8 \text{ pies} \times 8 \text{ oz/pie} = 64 \text{ oz}\) (which is 4 pounds).
- They have 48 oz of cherries (3 pounds) and 32 oz of apples (2 pounds).
- To meet the cherry requirement: \(4 \text{ pounds} - 3 \text{ pounds} = 1 \text{ pound of cherries needed}\)
- To meet the apple requirement: \(4 \text{ pounds} - 2 \text{ pounds} = 2 \text{ pounds of apples needed}\)
- This statement is **True**.
**Final True Statements:**
- Casey picked 2 times the weight of fruit that Karen picked.
- To make 8 pies, they would need 1 more pound of cherries and 2 more pounds of apples.