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, 3, 5, left parenthesis, 0, point, 4, 5, d, right parenthesis1.35(0.45d). Which description could explain what happened to the price of the share of stock?

Answer
Multiple Choice Answers
The price decreased by 0.55% and then increased by 35%
The price decreased by 55% and then increased by 35%
The price decreased by 55% and then increased by 0.35%
The price increased by 0.35% and then decreased by 0.45%

1 answer

To analyze the change in the selling price of the stock, we need to simplify the expression \(1.35(0.45d)\).

  1. First, calculate \(0.45d\): \[ 0.45d \] This represents a decrease of 55% from the original price \(d\) (since \(55% = 1 - 0.45\)).

  2. To find the new price after this decrease: \[ \text{Price after decrease} = 0.45d \]

  3. Now, we calculate \(1.35(0.45d)\): \[ 1.35(0.45d) = 0.6075d \] This means that after the decrease, the stock price becomes \(0.6075d\).

  4. We can interpret this:

    • The initial price \(d\) was reduced to \(0.45d\), which is a decrease of 55%.
    • Then, the price was multiplied by \(1.35\), which indicates an increase, but it applies to the already reduced price.

To answer the question, we compare the new price (\(0.6075d\)) relative to the original price (\(d\)):

  • The original price \(d\) decreased to \(0.6075d\), which means the overall decrease was more than just 55% due to the increase.

Therefore, the correct choice that explains what happened to the share price is:

The price decreased by 55% and then increased by 35%.