Question

y=2x+76, where x is time in years and y is the price of the textbook. this equation tells us that the textbook originally cost $76 and each year the cost went up $2. how many years will it take for the textbook to cost $100?
`y = 2x + 76`

Answer 1

We are given the following relationship:

`y=2x+76`

Where "y" is price and "x" is years. We are asked to find the number of years for the price to be $100. To do that, we will replace the value of "y" for 100, like this:

`100=2x+76`

Now, we will solve for "x", first by subtracting 76 on both sides:

`\begin{gathered} 100-76=2x+76-76 \\ 24=2x \end{gathered}`

Now we divide both sides by 2

`\begin{gathered} (24)/(2)=(2x)/(2) \\ 12=x \end{gathered}`

The value of "x" is 12, therefore, it is needed 12 years for the price to increase to $100.