- Translate the problem requirements: Bobby sold two shares for \(\$96\) each. One share gave him 20% profit, the other gave him 20% loss. We need to find his combined profit or loss on both shares.
- Calculate original cost of each share: Use the relationship between selling price, cost price, and profit/loss percentage to find what Bobby originally paid for each share.
- Determine total cost versus total revenue: Compare what Bobby paid for both shares combined against what he received from selling both shares.
- Calculate net profit or loss: Find the difference to determine Bobby's overall financial result.
Execution of Strategic Approach
1. Translate the problem requirements
Let's break down what we know in simple terms:
- Bobby sold TWO shares of stock
- He sold each share for exactly \(\$96\)
- On the FIRST share, he made a 20% profit
- On the SECOND share, he had a 20% loss
- We need to find out: did he make money overall, lose money overall, or break even?
Process Skill: TRANSLATE - Converting the word problem into clear mathematical relationships
2. Calculate original cost of each share
Now let's figure out what Bobby originally paid for each share.
For the share where he made a 20% profit:
If Bobby made a 20% profit, that means he sold it for 120% of what he paid for it.
In other words: Selling price = 120% of original cost
\(\$96 = 1.20 \times \mathrm{original\ cost}\)
\(\mathrm{Original\ cost} = \$96 \div 1.20 = \$80\)
For the share where he had a 20% loss:
If Bobby had a 20% loss, that means he sold it for 80% of what he paid for it.
In other words: Selling price = 80% of original cost
\(\$96 = 0.80 \times \mathrm{original\ cost}\)
\(\mathrm{Original\ cost} = \$96 \div 0.80 = \$120\)
3. Determine total cost versus total revenue
Now let's add up Bobby's total investment and total return:
Total amount Bobby originally paid:
First share cost: \(\$80\)
Second share cost: \(\$120\)
\(\mathrm{Total\ cost} = \$80 + \$120 = \$200\)
Total amount Bobby received from selling:
First share sold for: \(\$96\)
Second share sold for: \(\$96\)
\(\mathrm{Total\ revenue} = \$96 + \$96 = \$192\)
4. Calculate net profit or loss
To find Bobby's overall result, we compare what he spent versus what he received:
\(\mathrm{Net\ result} = \mathrm{Total\ revenue} - \mathrm{Total\ cost}\)
\(\mathrm{Net\ result} = \$192 - \$200 = -\$8\)
Since the result is negative, Bobby had a loss of \(\$8\) on the combined sale of both shares.
Final Answer
Bobby had a loss of \(\$8\) on the sale of both shares combined. This matches answer choice (C).
Common Faltering Points
Errors while devising the approach
- Misinterpreting what "profit" and "loss" percentages mean: Students often think that a 20% profit means Bobby paid 20% less than \(\$96\), or that a 20% loss means he paid 20% more than \(\$96\). The key insight they miss is that profit/loss percentages are calculated based on the original cost, not the selling price.
- Assuming the original costs were the same: Some students might assume both shares cost the same originally and try to work backwards from there, missing the fact that different percentage changes on the same selling price must mean different original costs.
- Focusing only on the percentages without calculating actual dollar amounts: Students might think "20% profit cancels out 20% loss" and conclude there's no net effect, without realizing that equal percentages applied to different base amounts don't cancel out.
Errors while executing the approach
- Setting up incorrect equations for original cost: When calculating original costs, students might write \(\$96 = \mathrm{Original\ cost} + 0.20 \times \mathrm{Original\ cost}\) instead of \(\$96 = 1.20 \times \mathrm{Original\ cost}\) for the profit scenario, leading to wrong original costs.
- Division errors when finding original costs: Students might make arithmetic mistakes when calculating \(\$96 \div 1.20 = \$80\) or \(\$96 \div 0.80 = \$120\), especially since these don't result in "nice" round numbers that are easy to verify.
- Using wrong decimal equivalents: Students might incorrectly convert percentages, such as using 0.20 instead of 1.20 for a 20% profit scenario, or 1.20 instead of 0.80 for a 20% loss scenario.
Errors while selecting the answer
- Forgetting to determine if the result is profit or loss: Students might correctly calculate the \(\$8\) difference but forget to check whether this represents a profit (positive) or loss (negative), potentially selecting answer choice (B) instead of (C).
- Confusing the direction of the calculation: Students might calculate \(\mathrm{Total\ cost} - \mathrm{Total\ revenue}\) instead of \(\mathrm{Total\ revenue} - \mathrm{Total\ cost}\), getting \(+\$8\) instead of \(-\$8\), leading them to think Bobby made a profit rather than a loss.
