Mark the number of hours after noon as x. Describe the prices of both stocks in terms of x to make an equation.
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Practice makes perfect
The price of Stock A at 9:00AM was $12.73. Since then the price has been decreasing at a rate of $0.06 per hour. At noon the price of Stock B was $13.48. It started decreasing at a rate of $0.14 per hour. We want to find the number of hours in which the prices of the stocks will be the same. Let's start with defining x. Then we will express the prices in terms of x.
x - the number of hours from noon
The price of Stock A at 9:00AM was $12.73. The price has been increasing at a rate of $0.06 per hour. Note that we marked the number of hours after noon as x. Since there are 3 hours between 9:00AM and noon, the price of Stock A will be 12.73 plus the number of hours from noon x plus 3 multiplied by 0.06. It is because between 9:00AM and noon the price has already increased 3 times.
Stock A's Price: 12.73+ 0.06(x+3)
Stock B's price at noon was $13.48. Then it decreases at a rate of 0.14 per hour. Therefore, the price of Stock B will be 13.48 minus the number of hours since noon x multiplied by 0.14.
Stock B's Price: 13.48- 0.14x
We want these prices to be equal, so we need to make an equation, which will have Stock A's price on the left-hand side, and Stock B's price on the right-hand side.
12.73+ 0.06(x+3) = 13.48- 0.14x
Now we will solve the obtained equation. We will use the inverse operations to combine like terms on both sides of the equals sign and solve for x.
