Question

The table shows the total cost c for the number of aquarium tickets purchased t. Write an equationthat can be used to find the cost c oft aquarium tickets. Use the equation and complete the table tofind the cost of 7 tickets.7Number of Tickets, tCost, cWrite an equation3$29.2510 12$97.50 $117.00(Use the operation symbols in the math palette as needed. Use integers or decimals for any numbers in the equatioDo not include the $ symbol in your answer.)

Answer 1

We can model the cost and number of tickets by a linear equation of the form

`c=mt+b`

Where c is the cost, t is the number of tickets.

m is the slope of the equation and b is the y-intercept.

First, let us find the slope which is given by

`m=(c_2-c_1)/(t_2-t_1)`

You can take any two pairs of values from the table.

`m=(117-97.50)/(12-10)=(19.5)/(2)=9.75`

The slope is 9.75 and the equation becomes

`c=9.75t+b`

Now we need to find the y-intercept (b)

Choose any one pair of values from the table and substitute them into the above equation and solve for b.

Let's choose (12, 117)

`\begin{gathered} c=9.75t+b \\ 117=9.75(12)+b \\ 117=117+b \\ b=117-117 \\ b=0 \end{gathered}`

The y-intercept is 0 so the equation is

`c=9.75t`

Now to find the cost of 7 tickets, simply substitute t = 7 into the above equation

`\begin{gathered} c=9.75t \\ c=9.75(7) \\ c=68.25 \end{gathered}`

Therefore, the cost of 7 tickets is $68.25