Question

The table represents the cost to eat at a buffet-style restaurant.Number ofPeople (p)2Cost (C)(including tax)27.5441.3155.0868.85345682.62Which equation could be used to calculate the cost. C, for any number of people, p, to eat at the restaurant?

Answer 1

We need to take the values of the table and check which of the options fit with the results.

In the first line of the table we have p=2 and C=27.54.

Using the equation in option A, for p=2 we would get:

`\begin{gathered} C=p+27.54 \\ C=2+27.54 \\ C=29.54 \end{gathered}`

Which is not value for C in the table. Thus we discard option A.

Using the equation for option B, for the value of p=2, we would get:

`\begin{gathered} C=13.77p \\ C=13.77(2) \\ C=27.54 \end{gathered}`

Which is indeed the value of the table.

To confirm, we try now with the next value of p, p=3, and check if we get the same result with equation B as with the table:

`\begin{gathered} C=13.77p \\ C=13.77(3) \\ C=41.31 \end{gathered}`

Which is also the value for C in the table.

Thus we confirm that option B is the correct equation