An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $1400 and her stock in Company B was worth $7100. The stock in Company A has decreased 5% since last year and the stock in Company B has decreased 9%. What was the total percentage decrease in the investor's stock account? Round your answer to the nearest tenth (if necessary).

  8.3% decrease

This value is approximate

Explanation:

The investor's account is worth 1400+7100 = 8500 dollars to start off.

A 5% decrease means we lose 5% of the value, but keep the remaining 95% of it. So company A's stock is now worth 0.95*1400 = 1330 dollars.

Company B has a 9% decrease in its stock price, so it keeps 100% - 9% = 91% of its value. It's value goes from $7100 to 0.91*7100 = 6461 dollars.

Next, we add up the values of each stock after the decreases take place. We get a total value of 1330+6461 = 7791

Recap so far:

The account has lost 8500-7791 = 709 dollars in value. Divide this over the original amount (8500) to find how much of a percent decrease happened.

709/8500 = 0.083  = 8.3% approximately

Slightly Alternative Method:

We can apply the percent change formula like so

A = old value = 8500

B = new value = 7791

C = percent change

C = [ (B-A)/A ] * 100%

C = [ (7791-8500)/8500 ] * 100%

C = (-709/8500) * 100%

C = -0.08341 * 100%

C = -8.341%

C = -8.3%

The negative C value indicates we have a percent decrease.

So C = -8.3% means the account's value has gone down by about 8.3%

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