a theatre has 1300 seats, rounded to 2 significant figures.the theatre sells 800 tickets, rounded to significant figure,480 child tickets,rounded to

Question

a theatre has 1300 seats, rounded to 2 significant figures.the theatre sells 800 tickets, rounded to significant figure,480 child tickets,rounded to 2 significant figures. the manager counts the number of tickets sold exactly and realises that the theatre has sold too many tickets. whta is the maximum number of tickets that could have been sold accidentally that dont have seats?

Answer 1

Hello,

If I understand the question correctly, the 800 tickets were rounded to one significant figure, and the 480 child tickets were rounded to two significant figures.

To answer the question, first we must find the maximum total number of tickets sold. To do so, we reverse the rounding operation, and assume that we rounded down so that the actual number of tickets is greater than the rounded number of tickets. For example, what is the maximum number that when rounded down to one significant figure gives 800? It would be 849, since if it was 850 it would be rounded to 900. Similarily, 484 would be the maximum number rounded down to two significant figures that gives 484.

Thus, the maximum number of tickets that could've been sold is 849+484 = 1333 tickets. Thus, the maximum number of tickets that could have been sold accidentally that don't have seats is 1333 -1300 = 33 tickets.