Question

Kevin bought stock in a company two years ago that was worth xx dollars. During the first year that he owned the stock, it increased by 23%. During the second year the value of the stock increased by 27%. Write an expression in terms of xx that represents the value of the stock after the two years have passed.

Answer 1

The expression that represents the value of the stock after two years is xx × 1.23 × 1.27, where xx is the original value of the stock.

Step-by-step explanation:

To find the expression that represents the value of the stock after two years, we will apply the percentage increases to the original value, xx, sequentially for each year.

During the first year, the value of the stock increases by 23%. This means the value after the first year is 1.23 times xx.

During the second year, the value of the stock increases by 27%. This means the value after the second year is 1.27 times the value after the first year.

Putting it all together, the expression in terms of xx that represents the value of the stock after two years is: xx * 1.23 * 1.27 = 1.5619 * xx

During the first year, the stock increased by 23%. To calculate this increase, we multiply the original value by 1 plus the percentage increase (expressed as a decimal):

First Year Value = xx × (1 + 0.23)

For the second year, the stock increased by 27%. To find the final value, we take the first year's value and multiply by 1 plus the second year's percentage increase:

Second Year Value = First Year Value × (1 + 0.27)

Plugging in the First Year Value, the expression for the value after two years is:

Final Value = xx × (1 + 0.23) × (1 + 0.27)

Therefore, the expression in terms of xx that represents the value of Kevin's stock after two years is xx × 1.23 × 1.27.