Gwen volunteered to work at the ticket booth for her school's Halloween carnival. The chart below gives the number of hours Gwen worked and the total number of tickets she sold.

t = 23h

why

The equation "t = 23h" is derived from the given table of values. In the table, it can be observed that for every hour Gwen worked, she sold 23 tickets. Therefore, the equation represents the relationship between the number of hours worked (h) and the number of tickets sold (t).

Solve:

−8+6x−(−12)=6x−16+2x
Responses

x=−6

x=−18

x=10

No Real Solutions

Let's solve the equation step by step:

-8 + 6x - (-12) = 6x - 16 + 2x

-8 + 6x + 12 = 6x - 16 + 2x

4 + 6x = 8x - 16

Rearrange the equation to get all the x terms on one side:

-6x + 4 = 2x - 16

Add 6x to both sides:

4 = 8x - 16

Add 16 to both sides:

20 = 8x

Divide both sides by 8:

20/8 = x

x = 2.5

Therefore, the solution to the equation is x = 2.5.

Based on the table, the equation for the relation between the number of hours Gwen worked (h) and the number of tickets she sold (t) is:

t = 23h

To write an equation for the relation between the number of hours Gwen worked and the number of tickets she sold, we need to determine the pattern in the given data.

From the table, we can observe that the number of tickets sold, denoted by "t," is directly proportional to the number of hours worked, denoted by "h." This means that the ratio of tickets to hours is constant.

To find this constant, we can pick any pair of data points from the table and calculate the ratio. Let's choose the first pair: (1, 23).

The ratio is determined by dividing the number of tickets by the number of hours:
t1/h1 = 23/1 = 23.

Now that we have the constant ratio, we can form the equation. The equation for the relation between the number of hours Gwen worked and the number of tickets she sold is:

t = 23h.

This equation states that the number of tickets, denoted by "t," is equal to 23 times the number of hours worked, denoted by "h."