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The price of Stock A at 9 a.m. was $15.75. Since then, the price has been increasing at the rate of $0.05 per hour. At noon, the price of Stock B was $16.53. It begins to decrease at the rate of $0.13 per hour. If the stocks continue to increase and decrease at the same rates, in how many hours will the prices of the stocks be the same?

Respuesta :

batolisis

Answer:

In approximately 3 hours time stock A will be the same price with Stock B

Step-by-step explanation:

Stock A increases at $ 0.05 per hour

stock A at 9 a.m = $ 15.75

stock  A at 12 noon = $ 15 .75 + $ 0.05 * 3

                                = $ 15.75 + $ 0.15 = $ 15.90

stock A in the next three hours again will be = $ 15.90 + $ 0.05 * 3

                                                                           = $15.90 + $ 0.15 = $ 16.05

Stock B at 12 noon = $ 16.53

stock B decreases at $ 0.13 per hour so in the next three hours stock B will be

= $ 16.53 - $ 0.13 * 3

= $ 16.53 - $0.39 = $16.14

fichoh

Using a system of linear equation, the price of Stock A and Stock B will be the same after 3.5 hours.

Stock A :

  • Initial price = $15.75
  • Rate of increase = 0.05

Stock B :

  • Rate of decrease = 16.53
  • Rate of decrease = 0.13

Price of stock A at noon :

15.75 + (0.05 × 3) = 15.90

Number of hours in which the stock price will be the same :

15.90 + 0.05t= 16.53 - 0.13t

Collect like terms

0.05t + 0.13t = 16.53 - 15.90

0.18t = 0.63

t = (0.63 ÷ 0.18)

t = 3.5

Therefore, the stocks will be of equal price after 3.5 hours.

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