Question
Multiple Choice Question
Molly's family has $3,000 set aside for an upcoming vacation. The family plans to spend
3/5
of this amount on gasoline for the drive and motel rooms along the way and
1/2
of the remainder on meals. How much does Molly's family plan to spend on meals?
A.
$600
B.
$900
C.
$1,200
D.
$1,500
Answers
GPT-4o mini
To determine how much Molly's family plans to spend on meals, we can break down the problem step by step.
1. **Calculate the amount spent on gasoline and motel rooms:**
\[
\text{Amount for gasoline and motel} = \frac{3}{5} \times 3000 = 1800
\]
2. **Calculate the remainder after gas and motel expenses:**
\[
\text{Remainder} = 3000 - 1800 = 1200
\]
3. **Calculate the amount spent on meals:**
\[
\text{Amount for meals} = \frac{1}{2} \times 1200 = 600
\]
Therefore, Molly's family plans to spend **$600** on meals.
The answer is **A. $600**.
1. **Calculate the amount spent on gasoline and motel rooms:**
\[
\text{Amount for gasoline and motel} = \frac{3}{5} \times 3000 = 1800
\]
2. **Calculate the remainder after gas and motel expenses:**
\[
\text{Remainder} = 3000 - 1800 = 1200
\]
3. **Calculate the amount spent on meals:**
\[
\text{Amount for meals} = \frac{1}{2} \times 1200 = 600
\]
Therefore, Molly's family plans to spend **$600** on meals.
The answer is **A. $600**.
What is the result of this calculation?
1/2 x 4/3 + 5/6 / 7/8 =
A.
1 27/48
B.
1 13/21
C.
1 33/42
D.
1 19/48
1/2 x 4/3 + 5/6 / 7/8 =
A.
1 27/48
B.
1 13/21
C.
1 33/42
D.
1 19/48
GPT-4o mini
To solve the expression \( \frac{1}{2} \times \frac{4}{3} + \frac{5}{6} \div \frac{7}{8} \), we will follow the order of operations.
1. **Calculate \( \frac{1}{2} \times \frac{4}{3} \)**:
\[
\frac{1}{2} \times \frac{4}{3} = \frac{1 \cdot 4}{2 \cdot 3} = \frac{4}{6} = \frac{2}{3} \quad (\text{simplified})
\]
2. **Calculate \( \frac{5}{6} \div \frac{7}{8} \)**:
To divide by a fraction, we multiply by its reciprocal:
\[
\frac{5}{6} \div \frac{7}{8} = \frac{5}{6} \times \frac{8}{7} = \frac{5 \cdot 8}{6 \cdot 7} = \frac{40}{42} = \frac{20}{21} \quad (\text{simplified})
\]
3. **Add the two results together**:
Now we have:
\[
\frac{2}{3} + \frac{20}{21}
\]
We need a common denominator to add these fractions. The least common multiple of 3 and 21 is 21.
Convert \( \frac{2}{3} \) to have a denominator of 21:
\[
\frac{2}{3} = \frac{2 \cdot 7}{3 \cdot 7} = \frac{14}{21}
\]
Now add the two fractions:
\[
\frac{14}{21} + \frac{20}{21} = \frac{14 + 20}{21} = \frac{34}{21}
\]
4. **Convert \( \frac{34}{21} \) to a mixed number**:
\[
34 \div 21 = 1 \quad \text{remainder } 13
\]
So, \( \frac{34}{21} = 1 \frac{13}{21} \).
Therefore, the result of the calculation is:
**B. \( 1 \frac{13}{21} \)**.
1. **Calculate \( \frac{1}{2} \times \frac{4}{3} \)**:
\[
\frac{1}{2} \times \frac{4}{3} = \frac{1 \cdot 4}{2 \cdot 3} = \frac{4}{6} = \frac{2}{3} \quad (\text{simplified})
\]
2. **Calculate \( \frac{5}{6} \div \frac{7}{8} \)**:
To divide by a fraction, we multiply by its reciprocal:
\[
\frac{5}{6} \div \frac{7}{8} = \frac{5}{6} \times \frac{8}{7} = \frac{5 \cdot 8}{6 \cdot 7} = \frac{40}{42} = \frac{20}{21} \quad (\text{simplified})
\]
3. **Add the two results together**:
Now we have:
\[
\frac{2}{3} + \frac{20}{21}
\]
We need a common denominator to add these fractions. The least common multiple of 3 and 21 is 21.
Convert \( \frac{2}{3} \) to have a denominator of 21:
\[
\frac{2}{3} = \frac{2 \cdot 7}{3 \cdot 7} = \frac{14}{21}
\]
Now add the two fractions:
\[
\frac{14}{21} + \frac{20}{21} = \frac{14 + 20}{21} = \frac{34}{21}
\]
4. **Convert \( \frac{34}{21} \) to a mixed number**:
\[
34 \div 21 = 1 \quad \text{remainder } 13
\]
So, \( \frac{34}{21} = 1 \frac{13}{21} \).
Therefore, the result of the calculation is:
**B. \( 1 \frac{13}{21} \)**.
Multiple Choice Question
Rashad purchased movie tickets for himself and two friends. After buying the tickets, he has $17 left over to buy snacks for the movie. Snack prices (including tax) are shown below:
Candy $1.50
Popcorn $4.00
Drink $2.75
Which of the following combinations of snacks could Rashad purchase?
A.
2 drinks and 3 popcorns
B.
3 popcorns and 3 candies
C.
4 popcorns and 1 candy
D.
4 drinks and 2 popcorns
GPT-4o mini
To determine which combination of snacks Rashad could purchase with his remaining $17, we can evaluate each option by calculating the total cost of the snacks in each combination.
**Snack Prices:**
- Candy: $1.50
- Popcorn: $4.00
- Drink: $2.75
### A. 2 drinks and 3 popcorns
- Cost = \( 2 \times 2.75 + 3 \times 4.00 \)
- Cost = \( 5.50 + 12.00 = 17.50 \)
### B. 3 popcorns and 3 candies
- Cost = \( 3 \times 4.00 + 3 \times 1.50 \)
- Cost = \( 12.00 + 4.50 = 16.50 \)
### C. 4 popcorns and 1 candy
- Cost = \( 4 \times 4.00 + 1 \times 1.50 \)
- Cost = \( 16.00 + 1.50 = 17.50 \)
### D. 4 drinks and 2 popcorns
- Cost = \( 4 \times 2.75 + 2 \times 4.00 \)
- Cost = \( 11.00 + 8.00 = 19.00 \)
### Summary of Costs:
- A: $17.50
- B: $16.50
- C: $17.50
- D: $19.00
The combinations that Rashad could afford (costing $17 or less) are:
- **B. 3 popcorns and 3 candies ($16.50)**
The other combinations (A and C) exceed Rashad's budget of $17, while D exceeds it as well.
Therefore, the correct answer is **B. 3 popcorns and 3 candies.**
**Snack Prices:**
- Candy: $1.50
- Popcorn: $4.00
- Drink: $2.75
### A. 2 drinks and 3 popcorns
- Cost = \( 2 \times 2.75 + 3 \times 4.00 \)
- Cost = \( 5.50 + 12.00 = 17.50 \)
### B. 3 popcorns and 3 candies
- Cost = \( 3 \times 4.00 + 3 \times 1.50 \)
- Cost = \( 12.00 + 4.50 = 16.50 \)
### C. 4 popcorns and 1 candy
- Cost = \( 4 \times 4.00 + 1 \times 1.50 \)
- Cost = \( 16.00 + 1.50 = 17.50 \)
### D. 4 drinks and 2 popcorns
- Cost = \( 4 \times 2.75 + 2 \times 4.00 \)
- Cost = \( 11.00 + 8.00 = 19.00 \)
### Summary of Costs:
- A: $17.50
- B: $16.50
- C: $17.50
- D: $19.00
The combinations that Rashad could afford (costing $17 or less) are:
- **B. 3 popcorns and 3 candies ($16.50)**
The other combinations (A and C) exceed Rashad's budget of $17, while D exceeds it as well.
Therefore, the correct answer is **B. 3 popcorns and 3 candies.**