The original selling price of a share of stock was dd dollars. The selling price for a share of the same stock at a later date was represented by the expression 1, point, 7, 5, left parenthesis, 0, point, 1, d, right parenthesis1.75(0.1d). Which description could explain what happened to the price of the share of stock?

Question

Answer
Multiple Choice Answers
The price increased by 0.75% and then decreased by 0.1%
The price increased by 75% and then decreased by 0.1%
The price decreased by 90% and then increased by 75%
The price decreased by 0.9% and then increased by 175%

Answer 1

To analyze the expression \(1.75(0.1d)\) and understand what happened to the price of the share of stock, we can break it down.

1. Understanding the Initial Value:

   • The original price of the stock is \(d\).

2. Interpretation of the Expression \(1.75(0.1d)\):

   • The term \(0.1d\) represents 10% of the original price \(d\).
   • Now, multiplying by \(1.75\) means we take \(1.75\) times \(0.1d\), which is: \[ 1.75 \times 0.1d = 0.175d \]
   • This is the new price of the stock, which is \(0.175d\).

3. Comparison to Original Price:

   • To find out how this price compares to the original price:
     • The new price \(0.175d\) is 17.5% of the original price \(d\).

4. Calculating Changes in Price Percentage:

   • The decrease in price from \(d\) to \(0.175d\):
     • The decrease in price is: \[ d - 0.175d = 0.825d \]
     • To find the percentage decrease: \[ \frac{0.825d}{d} \times 100 = 82.5% \]
   • Thus, the price decreased by 82.5%.

Given these calculations, we need to compare it to the options provided:

• The Price Increased by 0.75% and Then Decreased by 0.1%: This is incorrect.
• The Price Increased by 75% and Then Decreased by 0.1%: This is incorrect.
• The Price Decreased by 90% and Then Increased by 75%: This is incorrect; the decrease was only 82.5%.
• The Price Decreased by 0.9% and Then Increased by 175%: This is incorrect; we calculated an 82.5% decrease.

Conclusion:

None of the provided choices accurately represent what happened to the share price based on the calculations derived from the expression. The price actually decreased significantly (by 82.5%) without any increase that matches the options given. It appears there might be a miscalculation or misinterpretation in the options provided.