A local zoo found that if the price of admission was $17, the attendance was about 1850 customers per week. When the price of admission was dropped to $13,attendance increased to about 2700 per week. Write a linear equation for the attendance in terms of the price,p. (A = mp+b)

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CadeeF15650 CadeeF15650 · Answer 1 · 2022-10-31T04:06:22-04:00

It is given that the general equation is:

[tex]A=mp+b[/tex]

Here A is the number of people attending and p is the price of ticket.

Find the values of m and b by the conditions.

When A=1850, p=17 so it follows:

[tex]1850=17m+b\ldots(i)[/tex]

When A=2700, p=13 so it follows:

[tex]2700=13m+b\ldots(ii)[/tex]

Subtract (ii) from (i) to get:

[tex]\begin{gathered} 1850-2700=17m-13m \\ m=\frac{1850-2700}{4}=\frac{-425}{2}=-212.5 \end{gathered}[/tex]

Substitute the value of m in (i) to get:

[tex]\begin{gathered} 1850=17(-\frac{425}{2})+b \\ b=\frac{10925}{2}=5462.5 \end{gathered}[/tex]

So the equation becomes:

[tex]\begin{gathered} A=\frac{-425}{2}p+\frac{10925}{2} \\ 2A=-425p+10925 \end{gathered}[/tex]

Hence the linear equation is 2A=-425p+10925.