An intensive effort was made to expand the database of alumni names for a certain high school. The number of...

1. Translate the problem requirements: Clarify what "increased by 1,300 percent of the original number" means - this is the increase amount added to the original, not the final total
2. Calculate the increase amount: Find 1,300% of the original 1,500 names to determine how many names were added
3. Find the expanded database total: Add the calculated increase to the original number of names

Execution of Strategic Approach

1. Translate the problem requirements

Let's start by understanding what this problem is really asking us. The key phrase here is "increased by 1,300 percent of the original number."

Think of it this way: if you have $100 in your wallet and someone gives you an additional $50 (which is 50% of your original $100), you now have $150 total. The "increase" is the extra amount added on top of what you started with.

In our problem:

• We start with 1,500 names (our original amount)
• The database "increased by" 1,300% of the original
• This means we're adding 1,300% of 1,500 names to our original 1,500

So we need to find: Original names + Increase = Final total

Process Skill: TRANSLATE - Converting the percentage language into a clear mathematical relationship

2. Calculate the increase amount

Now we need to find exactly how many names were added to the database.

The increase is 1,300% of the original 1,500 names.

Let's think about this step by step:

• 100% of 1,500 = 1,500 (the whole original amount)
• 1,300% means 13 times as much as 100%
• So 1,300% of 1,500 = \(13 \times 1500\)

Calculating: \(13 \times 1500 = 19500\)

This means 19,500 new names were added to the database.

Technical notation: \(1300\% \times 1500 = 13.00 \times 1500 = 19500\)

3. Find the expanded database total

Now we can find the total number of names in the expanded database.

We take what we started with and add what was gained:

• Original number of names: 1,500
• Number of names added: 19,500
• Total in expanded database: \(1500 + 19500 = 21000\)

Let's verify this makes sense: We added 19,500 names to an original 1,500, giving us 21,000 total names. The increase (19,500) is indeed much larger than the original (1,500), which makes sense for a 1,300% increase.

4. Final Answer

The expanded database contains 21,000 names.

Looking at our answer choices:

1. 1,950 - Too small
2. 2,800 - Too small
3. 16,300 - This would be just the increase, not the total
4. 19,500 - This is just the increase amount, not the final total
5. 21,000 - This matches our calculation

The correct answer is E. 21,000

Common Faltering Points

Errors while devising the approach

1. Misinterpreting "increased by X percent" vs "increased to X percent"
Students often confuse these two phrases. "Increased by 1,300%" means adding 1,300% of the original to the original amount. However, students might incorrectly think it means the final amount is 1,300% of the original (which would be "increased to 1,300%"). This fundamental misunderstanding would lead them to calculate \(1300\% \times 1500 = 19500\) as the final answer instead of recognizing this as just the increase amount.

2. Converting percentage incorrectly
When seeing 1,300%, students might struggle with the conversion to decimal form. Some may incorrectly convert 1,300% to 1.3 instead of 13.0, thinking that you just move the decimal point one place. This would lead to calculating the increase as \(1.3 \times 1500 = 1950\) instead of the correct \(13 \times 1500 = 19500\).

Errors while executing the approach

1. Arithmetic errors in multiplication
When calculating \(13 \times 1500\), students might make computational errors. Common mistakes include getting 16,500 instead of 19,500, or making errors when handling the zeros. These calculation mistakes would carry through to the final answer, leading to incorrect totals.

2. Forgetting to add the original amount
Even if students correctly calculate that 19,500 names were added, they might forget that the question asks for the total in the expanded database. They could stop at the increase amount (19,500) and not add it to the original 1,500 names to get the final total of 21,000.

Errors while selecting the answer

1. Selecting the increase amount instead of the total
Students who correctly calculate the increase as 19,500 might select answer choice D (19,500) without realizing this represents only the additional names, not the total names in the expanded database. The question specifically asks "How many names were in the expanded database?" which requires the sum of original plus increase.