Andrew started saving at the beginning of the year and had saved $240 by the end of the year. He...

1. Translate the problem requirements: Andrew saved $240 in year 1, and $540 total by end of year 2. We need to find the percent increase in his second year savings compared to his first year savings. This means we need to find how much he saved in year 2 alone, then compare it to year 1.
2. Calculate second year savings amount: Determine how much Andrew saved specifically during the second year by subtracting his first year total from his two-year total.
3. Set up the percent increase comparison: Use the first year savings as the base amount and the second year savings as the new amount to find the percent increase.
4. Calculate the percent increase: Apply the percent increase formula using the values from the previous steps and match to the closest answer choice.

Execution of Strategic Approach

1. Translate the problem requirements

Let's break down what Andrew did with his savings:

• At the end of year 1: Andrew had saved $240 total
• At the end of year 2: Andrew had saved $540 total

The question asks us to find the percent increase in the amount Andrew saved during the second year compared to what he saved during the first year.

This means we need to compare two specific amounts:

• Amount saved in year 1 only: $240
• Amount saved in year 2 only: We need to calculate this

Process Skill: TRANSLATE - Converting the problem language into clear mathematical understanding of what we're comparing

2. Calculate second year savings amount

To find how much Andrew saved specifically during the second year, we need to think about this logically:

If Andrew had $240 at the end of year 1, and $540 at the end of year 2, then the amount he saved during year 2 alone is:

Amount saved in year 2 = Total after 2 years - Total after 1 year
Amount saved in year 2 = \(\$540 - \$240 = \$300\)

So Andrew saved $300 during the second year.

3. Set up the percent increase comparison

Now we have the two amounts we need to compare:

• Year 1 savings: $240 (this is our baseline)
• Year 2 savings: $300 (this is what we're comparing to the baseline)

We want to find: How much more did Andrew save in year 2 compared to year 1, expressed as a percentage?

The increase in savings = $300 - $240 = $60

So Andrew saved $60 more in year 2 than in year 1.

4. Calculate the percent increase

To find the percent increase, we ask: "$60 is what percent of the original $240?"

Percent increase = (Increase ÷ Original amount) × 100%
Percent increase = \((\$60 ÷ \$240) \times 100\%\)
Percent increase = \(\frac{1}{4} \times 100\%\)
Percent increase = \(0.25 \times 100\% = 25\%\)

Looking at our answer choices, 25% matches choice B exactly.

Final Answer

The percent increase in Andrew's second year savings compared to his first year savings is 25%.

Answer: B. 25%

Common Faltering Points

Errors while devising the approach

1. Misunderstanding what amounts to compare: Students often confuse what the question is asking for. They might think they need to compare the total amount saved ($540) to the first year amount ($240), rather than comparing the amount saved during the second year ($300) to the amount saved during the first year ($240).

2. Confusing cumulative vs. annual savings: Students may not clearly distinguish between cumulative totals ("had saved $240 by end of year 1") and individual year amounts ("amount saved during the second year"). This leads to setting up the wrong comparison.

Errors while executing the approach

1. Arithmetic errors in subtraction: When calculating the amount saved in year 2 ($540 - $240), students might make simple arithmetic mistakes, getting $200 or $320 instead of $300.

2. Percent calculation errors: Students often struggle with the percent increase formula. They might calculate $60/$300 instead of $60/$240, or forget to multiply by 100, or make errors when converting the fraction 1/4 to 25%.

3. Using wrong baseline for percentage: Students might use the second year amount ($300) as the denominator instead of the first year amount ($240), calculating \((\$60/\$300) \times 100\% = 20\%\) instead of the correct 25%.

Errors while selecting the answer

1. Selecting based on wrong calculation: If students calculated the percent increase of total savings ($540 vs $240), they would get \(125\%\) and might select choice E instead of the correct answer B.