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 0, point, 2, 5, left parenthesis, 1, point, 3, 5, d, right parenthesis0.25(1.35d). Which description could explain what happened to the price of the share of stock?

Question

Answer
Multiple Choice Answers
The price decreased by 0.75% and then increased by 135%
The price decreased by 25% and then increased by 35%
The price decreased by 75% and then increased by 35%
The price increased by 0.35% and then decreased by 0.75%

Answer 1

To analyze the expression \(0.25(1.35d)\), we can interpret what happens to the original selling price \(d\).

1. Calculating the 25% decrease:

   • A decrease of 25% means you keep 75% of the original price. Mathematically, this can be represented as: \[ d - 0.25d = 0.75d \]
   • Therefore, after a decrease of 25%, the new price would be \(0.75d\).

2. Calculating the 35% increase:

   • After applying a 35% increase to \(0.75d\), the new price becomes: \[ 0.75d + 0.35(0.75d) = 0.75d(1 + 0.35) = 0.75d(1.35) = 1.0125d \]

Now, let's see how much this increase corresponds to. We find the final price as: \[ 0.25(1.35d) = 0.25(1.35)d = 0.3375d \]

This calculation does not match \(1.0125d\).

So, let's clarify the expression: The expression \(0.25(1.35d)\) suggests that from the original price \(d\), we first decreased by 25%, leaving us with \(0.75d\), and then increased that amount by 35%.

Now, let's analyze the choices:

1. The price decreased by 0.75% and then increased by 135% — Incorrect.
2. The price decreased by 25% and then increased by 35% — Correct.
3. The price decreased by 75% and then increased by 35% — Incorrect.
4. The price increased by 0.35% and then decreased by 0.75% — Incorrect.

The correct answer is: The price decreased by 25% and then increased by 35%.