Gabriella purchased d dollars of two different stocks exactly one year ago. Currently, stock A has increased by 5%, and stock B has decreased by 5%.

Which of the following expressions could be used to represent the current value of each of Gabriella's stock accounts?

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1 answer

Let's break down Gabriella's investments to understand how to calculate the current values of her stocks.

Assume Gabriella invested an amount \( a \) dollars in stock A and \( b \) dollars in stock B, with the total investment being \( d \) dollars:

\[ a + b = d \]

  1. For Stock A: Since stock A increased by 5%, the current value of stock A can be calculated as follows:

\[ \text{Current Value of Stock A} = a + 0.05a = 1.05a \]

  1. For Stock B: Since stock B decreased by 5%, the current value of stock B can be calculated as follows:

\[ \text{Current Value of Stock B} = b - 0.05b = 0.95b \]

  1. Total Current Value: The total current value of Gabriella's stocks can be represented as:

\[ \text{Total Current Value} = \text{Current Value of Stock A} + \text{Current Value of Stock B} = 1.05a + 0.95b \]

Given that \( a + b = d \), we could express the total current value using the original total investment (though it would still depend on \( a \) and \( b \)).

However, if you are looking for expressions to represent the current value of each stock account individually, you have:

  • Current value of stock A: \( 1.05a \)
  • Current value of stock B: \( 0.95b \)

Those are the expressions that could be used to represent the current value of Gabriella's stock accounts.