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An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $6750 and her stock in Company B was worth $4210. The stock in Company A has decreased 18% since last year and the stock in Company B has decreased 20%. What was the total percentage decrease in the investor's stock account? Round your answer to the nearest tenth (if necessary).

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gh8186

Answer:

3.5%

Step-by-step explanation:

1. calculate starting total

[tex]6750 + 4210=10960[/tex]

starting amount = $10,960

2. calculate stock    A2's value

  • decreased by 18%

to make the percentage usable in this equation we need to divide it by 100 to get it in decimal form. ⇒ [tex]\frac{18}{100} = 0.18[/tex]

  • multiply stock A1 by perctage decimal to get the amount decreased

[tex]6750(0.18)=1215[/tex] ($1,215)

  • subtract stock A1 by decreased amount to get stock A2's value

[tex]6750-1215=5535[/tex]

A2 = $5,535

3. calculate stock    B2's value

  • increased by 20%

to make the percentage usable in this equation we need to divide it by 100 to get it in decimal form. ⇒ [tex]\frac{20}{100} = 0.20[/tex]

  • multiply stock B1 by perctage decimal to get the amount increased

[tex]4210(0.20)=842[/tex] ($842)

  • add stock B1 with increased amount to get stock B2's value

[tex]4210+842=5052[/tex]

B2 = $5,052

4. get new amount of account

[tex]5052+5535=10587[/tex]

new amount = $10,587

5. find percentage decrease of starting amount to new amount

  • divide starting amount by the new amount

[tex]\frac{10960}{10587} = 1.03523188816[/tex]

  • then subtract by 1

[tex]1.03523188816-1 =0.03523188816[/tex]

  • multiply by 100 to convert to percentage form

[tex]0.03523188816(100) =3.523188816[/tex]

  • and round to nearest tenth

answer is ≈ 3.5%

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