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, 5, 5, left parenthesis, 0, point, 6, d, right parenthesis1.55(0.6d). Which description could explain what happened to the price of the share of stock?

Question

Answer
Multiple Choice Answers
The price decreased by 40% and then increased by 55%
The price increased by 155% and then decreased by 40%
The price decreased by 60% and then increased by 155%
The price decreased by 40% and then increased by 0.55%

Answer 1

To analyze the price change of the stock, we can break down the expression \(1.55(0.6d)\).

1. Calculate the price after the first change:

   • The term \(0.6d\) indicates that the price of the share decreased to 60% of the original price \(d\). This is equivalent to a decrease of 40%.
   • Mathematically, \(0.6d = d - 0.4d\).

2. Calculate the price after the second change:

   • The term \(1.55(0.6d)\) indicates that the new price after the first decrease is then increased by 55%.
   • This means the price becomes \(1.55\) times the decreased price \(0.6d\).

Putting this together:

• The price first decreased by 40% (to \(0.6d\)), and then increased by 55% of that decreased price.

Given these calculations, the correct description of what happened to the price of the share of stock is:

The price decreased by 40% and then increased by 55%.

However, it should be noted that while the problem didn't have this exact answer, it might have misphrased one of the answer choices. Based on what we determined from the calculations, the option closest to our analysis is:

The price decreased by 40% and then increased by 155%.

This indicates possibly an error in the provided answers since the 155% increase could represent an overall price reflection based on total gains from the original. The answer that fits our mathematic breakdown is:

The price decreased by 40% and then increased by 55%.

Considering the choices given, please verify if "decreased by 40% then increased by 155%" might be a typographical error in the exam. However, technically, the rise is 55% of the previously reduced price and should reflect accordingly.