Sample Calculated Formula Question

If a small glass contains 8 ounces of water, and a large glass contains 12 ounces of water, what is the total number of ounces in 3 large and 4 small glasses of water?

Question

Sample Calculated Formula Question

If a small glass contains 8 ounces of water, and a large glass contains 12 ounces of water, what is the total number of ounces in 3 large and 4 small glasses of water?

BlackTom AI · Accepted Answer

Each small glass holds 8 ounces and each large glass holds 12 ounces, so total volume is the sum of (number of glasses × ounce per glass).

1. Relevant knowledge and concepts
- Multiplication to find total amount from a unit rate: total = quantity × unit amount.
- Addition to combine totals from different groups.
- Consistent units (all in ounces).

2. Complete reasoning, step by step
- Compute the total ounces contributed by the large glasses.
- Compute the total ounces contributed by the small glasses.
- Add those two totals to obtain the overall number of ounces.

3. Intermediate calculation steps
- Large glasses: 3 large × 12 ounces/large = 3 × 12 = 36 ounces.
- Small glasses: 4 small × 8 ounces/small = 4 × 8 = 32 ounces.
- Total ounces: 36 ounces + 32 ounces = 68 ounces.

4. Why the correct answer is correct
- Each group (large and small) contributes independently and proportionally to its count. Multiplying the count by the per-glass ounces gives exact totals for each group; adding them yields the combined total. The arithmetic 36 + 32 = 68 follows directly and uses no approximations or assumptions, so 68 ounces is exact.

5. Common incorrect approaches and why they are wrong
- Adding counts first (3 + 4 = 7) then multiplying by a single glass size (for example 7 × 8 = 56 or 7 × 12 = 84) is wrong because glasses are not all the same size.
- Averaging glass sizes without weighting by counts would also be unnecessary and error-prone here.
- Forgetting units or mixing ounces with other units would produce incorrect results.

6. Conclusion
The total number of ounces in 3 large and 4 small glasses is 68 ounces. This matches the provided correct answer: 68.

Sample Calculated Formula Question If a small glass contains 8 ounces of water, and a large glass contains 12 ounces of water, what is the total number of ounces in 3 large and 4 small glasses of water?简答题

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