On Monday, the opening price of a certain stock was $100 per share and its closing price was $110 per...

1. Translate the problem requirements: We need to track a stock's price from Monday opening (\(\$100\)) through daily percentage changes to find the overall percent change by Wednesday closing. Monday: opens at \(\$100\), closes at \(\$110\). Tuesday: closes \(10\%\) less than Monday's close. Wednesday: closes \(4\%\) greater than Tuesday's close.
2. Calculate Tuesday's closing price: Apply the \(10\%\) decrease to Monday's closing price of \(\$110\) to find Tuesday's closing value.
3. Calculate Wednesday's closing price: Apply the \(4\%\) increase to Tuesday's closing price to find the final stock price.
4. Determine overall percent change: Compare Wednesday's closing price to Monday's opening price (\(\$100\)) to calculate the total percentage change over the three-day period.

Execution of Strategic Approach

1. Translate the problem requirements

Let's break down what's happening with this stock over three days in plain English:

Monday: The stock starts the day at \(\$100\) (opening price) and ends at \(\$110\) (closing price)

Tuesday: The stock closes \(10\%\) lower than Monday's closing price of \(\$110\)

Wednesday: The stock closes \(4\%\) higher than Tuesday's closing price

Our goal is to find how much the stock changed from Monday's opening (\(\$100\)) to Wednesday's closing price.

Process Skill: TRANSLATE - Converting the word problem into clear mathematical steps we can follow

2. Calculate Tuesday's closing price

Tuesday's closing price is \(10\%\) less than Monday's closing price of \(\$110\).

Let's think about this step by step:

• Monday's closing price: \(\$110\)
• \(10\%\) decrease means we keep \(90\%\) of the original price
• \(90\%\) of \(\$110 = 0.90 \times \$110 = \$99\)

So Tuesday's closing price is \(\$99\).

3. Calculate Wednesday's closing price

Wednesday's closing price is \(4\%\) greater than Tuesday's closing price of \(\$99\).

Let's work through this:

• Tuesday's closing price: \(\$99\)
• \(4\%\) increase means we have \(104\%\) of the original price
• \(104\%\) of \(\$99 = 1.04 \times \$99 = \$102.96\)

So Wednesday's closing price is \(\$102.96\).

4. Determine overall percent change

Now we compare Wednesday's closing price to Monday's opening price to find the total change.

Starting point: Monday opening = \(\$100\)

Ending point: Wednesday closing = \(\$102.96\)

The stock went from \(\$100\) to \(\$102.96\), which is an increase of \(\$2.96\).

To find the percent change:

• Change in price = \(\$102.96 - \$100 = \$2.96\)
• Percent change = (Change ÷ Original price) × \(100\%\)
• Percent change = \((\$2.96 ÷ \$100) \times 100\% = 2.96\%\)

Since \(2.96\%\) rounds to approximately \(3\%\), this represents an increase of about \(3\%\).

Final Answer

The stock price increased from \(\$100\) to approximately \(\$103\), representing an increase of about \(3\%\).

Answer: D. An increase of 3%

Common Faltering Points

Errors while devising the approach

1. Misidentifying the comparison points: Students often confuse what they need to compare. The question asks for the change from Monday's opening price to Wednesday's closing price, but students might mistakenly compare Monday's closing price to Wednesday's closing price, or use other incorrect starting/ending points.

2. Misunderstanding percentage decrease language: When the problem states "10 percent less than," students might incorrectly subtract 10 from the price (making it \(\$100\)) rather than calculating \(90\%\) of the original price (\(\$99\)). This linguistic confusion between absolute decrease versus percentage decrease is common.

Errors while executing the approach

1. Percentage calculation errors: Students frequently make mistakes when calculating percentages, such as computing \(90\%\) of \(\$110\) as \(\$110 - \$10 = \$100\) instead of \(\$110 \times 0.90 = \$99\), or calculating \(104\%\) of \(\$99\) incorrectly.

2. Compounding the percentage changes incorrectly: Some students attempt to simply add and subtract the percentages (\(-10\% + 4\% = -6\%\)) rather than calculating each day's price step by step. This shortcut fails because the percentages apply to different base amounts.

3. Arithmetic errors in final calculations: Students may correctly find Wednesday's closing price as \(\$102.96\) but then make errors when calculating the percentage change, such as computing \((\$102.96 - \$100)/\$100\) incorrectly or making rounding mistakes.

Errors while selecting the answer

1. Forgetting to determine increase vs. decrease: After calculating that the change is approximately \(3\%\), students might select "A decrease of 3%" if such an option existed, forgetting to check whether the final price is higher or lower than the starting price.