An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $2150 and her stock in Company B was worth $4000. The stock in Company A has decreased 2% since last year and the stock in Company B has decreased 25%. What was the total percentage decrease in the investor's stock account? Round your answer to the nearest tenth (if necessary).
The stock in Company A decreased by 2%, which means it is now worth 98% of what it was worth last year (100% - 2% = 98%).
The stock in Company B decreased by 25%, which means it is now worth 75% of what it was worth last year (100% - 25% = 75%).
The value of the stock in Company A has decreased to 0.98 * $2150 = $2107.
The value of the stock in Company B has decreased to 0.75 * $4000 = $3000.
The total value of the investor's stock account is now $2107 + $3000 = $5107.
The total decrease in the investor's stock account is $5107 - ($2150 + $4000) = $95.
The percentage decrease is $95 / ($2150 + $4000) * 100% = 1.3% (rounded to the nearest tenth). Answer: \boxed{1.3}.
To find the total percentage decrease in the investor's stock account, we need to calculate the individual decreases in the stock values and then combine them.
Let's start by calculating the decrease in stock A. Since it decreased by 2%, we can find the decrease amount by multiplying the original value by 2% (or 0.02):
Decrease in stock A = $2150 * 0.02 = $43
Now let's calculate the decrease in stock B. Since it decreased by 25%, we can find the decrease amount by multiplying the original value by 25% (or 0.25):
Decrease in stock B = $4000 * 0.25 = $1000
To find the total decrease in the investor's stock account, we add the individual decreases:
Total decrease = Decrease in stock A + Decrease in stock B
= $43 + $1000
= $1043
To find the total percentage decrease, we need to divide the total decrease by the sum of the original stock values and then multiply by 100:
Total percentage decrease = (Total decrease / Sum of original stock values) * 100
= ($1043 / ($2150 + $4000)) * 100
= ($1043 / $6150) * 100
≈ 16.96%
Therefore, the total percentage decrease in the investor's stock account is approximately 16.96%.
To find the total percentage decrease in the investor's stock account, we need to calculate the individual percentage decreases for both stocks and then sum them up.
Step 1: Calculate the decrease in stock value for Company A:
2% of $2150 = 0.02 * $2150 = $43
Step 2: Calculate the new value for stock in Company A:
$2150 - $43 = $2107
Step 3: Calculate the decrease in stock value for Company B:
25% of $4000 = 0.25 * $4000 = $1000
Step 4: Calculate the new value for stock in Company B:
$4000 - $1000 = $3000
Step 5: Calculate the total decrease in the investor's stock account:
$2150 - $2107 + $4000 - $3000 = $43 + $1000 = $1043
Step 6: Calculate the total percentage decrease:
Total percentage decrease = (Total decrease / Total initial value) * 100
= ($1043 / ($2150 + $4000)) * 100
= ($1043 / $6150) * 100
= 0.1695 * 100
= 16.9%
Therefore, the total percentage decrease in the investor's stock account is approximately 16.9%.