Loading...
On Monday, the opening price of a certain stock was $100 per share and its closing price was $110 per share. On Tuesday the closing price of the stock was 10 percent less than its closing price on Monday, and on Wednesday the closing price of the stock was 4 percent greater than its closing price on Tuesday. What was the approximate percent change in the price of the stock from its opening price on Monday to its closing price on Wednesday?
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
Tuesday's closing price is \(10\%\) less than Monday's closing price of \(\$110\).
Let's think about this step by step:
So Tuesday's closing price is \(\$99\).
Wednesday's closing price is \(4\%\) greater than Tuesday's closing price of \(\$99\).
Let's work through this:
So Wednesday's closing price is \(\$102.96\).
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:
Since \(2.96\%\) rounds to approximately \(3\%\), this represents an increase of about \(3\%\).
The stock price increased from \(\$100\) to approximately \(\$103\), representing an increase of about \(3\%\).
Answer: D. An increase of 3%
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.
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.
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.