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.)

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AaravG3152 AaravG3152 · Answer 1 · 2022-10-25T16:39:50+02:00

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

[tex]c=mt+b[/tex]

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

[tex]m=\frac{c_2-c_1}{t_2-t_1}[/tex]

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

[tex]m=\frac{117-97.50}{12-10}=\frac{19.5}{2}=9.75[/tex]

The slope is 9.75 and the equation becomes

[tex]c=9.75t+b[/tex]

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)

[tex]\begin{gathered} c=9.75t+b \\ 117=9.75(12)+b \\ 117=117+b \\ b=117-117 \\ b=0 \end{gathered}[/tex]

The y-intercept is 0 so the equation is

[tex]c=9.75t[/tex]

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

[tex]\begin{gathered} c=9.75t \\ c=9.75(7) \\ c=68.25 \end{gathered}[/tex]

Therefore, the cost of 7 tickets is $68.25