Question

A community recreation center has collected a total of 618 donated tickets for free ice cream. Beginning on the second day of summer vacation, the recreation center randomly selects 7 children to each receive one of the free ice cream tickets. Assuming the recreation center continues this pattern of giving away tickets to 7 children each day, which explicit formula shows the number of ice cream tickets remaining at the end of the day, after n number of days?

Answer 1

We can create a table listing few of the values to spot the pattern.
$\centering \label{my-label} \begin{tabular}{lll} Day & Number of tickets & Different form \\ 1 & 618-7 & 618-1\cdot7 \\ 2 & 618-14 & 618-2\cdot7 \\ 3 & 618-21 & 618-3\cdot7 \end{tabular} \end{table}$
It is clear from the table that formula we need is:
$N=618-n\cdot7$
Where n is number of a day we are looking at and N is number of tickets left.