9. higher order thinking the price of stock a at 9 a.m. was $15.75. since then, the price has been…

9. higher order thinking 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?

9. higher order thinking 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?

Answer

Explanation:

Step1: Calculate Stock A's price at noon

From 9 A.M. to noon is 3 hours. Stock A's price at noon is $15.75+0.05\times3=15.75 + 0.15=15.9$.

Step2: Set up an equation for when the stock prices are equal

Let $t$ be the number of hours after noon when the prices are the same. The price of Stock A after $t$ hours is $15.9 + 0.05t$, and the price of Stock B after $t$ hours is $16.53-0.13t$. Set them equal: $15.9 + 0.05t=16.53-0.13t$.

Step3: Solve the equation for $t$

Add $0.13t$ to both sides: $15.9+0.05t + 0.13t=16.53-0.13t+0.13t$, which simplifies to $15.9 + 0.18t=16.53$. Then subtract 15.9 from both sides: $0.18t=16.53 - 15.9=0.63$. Divide both sides by 0.18: $t=\frac{0.63}{0.18}=3.5$.

Answer:

3.5