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%.

Question

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

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Answer 1

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:

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

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

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

3. 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.