Question

Question:

In the equation P = 2x + 7, P represents the price, in dollars, of tickets to a concert x hours after they go on sale. When will the price exceed $20.00?

1. Describe in words how the equation can be used to solve the problem.

2. Draw a graphical representation of the price equation, and illustrate how a solution could be found that way.

Answer 1

1. This equation can be used to help solve the problem by plugging in numbers for x. Whatever answer for x gives a price that is more than $20.00 is the answer for the number of tickets that have to be sold in order to exeed $20.00.

2. This equation has the same format as an equation in slope intercept form. This makes it easy to graph.The y intercept will be 7 and the slope is 2. Using this information, it is easy to graph the equation and find a solution. The graph should look like the image I attached to this answer.

Answer 2

Let

P-------> the price in dollars of tickets

x------> the number of hours

we know that

`P=2x+7` -------> equation A

When will the price exceed $20.00?

Part 1) Describe in words how the equation can be used to solve the problem

Substitute the value of P equal to
`\$20.00` in the equation A and find the value of x

so

For
`P=\$20.00`

substitute in equation A

`20=2x+7`

`2x=20-7`

`2x=13`

`x=6.5\ hours`

therefore

the answer Part 1) is

the price exceed
`\$20.00` when the time exceed
`6.5\ hours`

Part 2) Draw a graphical representation of the price equation, and illustrate how a solution could be found that way.

using a graphing tool

Draw the equation of the lines

`P=2x+7`

`P=20`

the solution is the intersection both graphs

see the attached figure

the solution is the point
`(6.5, 20)`

that means

for
`x=6.5\ hours`

`P=\$20.00`