Question

Lin has a number of Playbills from the Broadway shows that he has attended over many years all collected in one big box. One day he took them all out and started arranging them into equal‐sized piles, with the intention of putting them into binders with the same number of Playbills in each binder. First he arranged them all into four piles, but there was one Playbill left over. So then he tried five piles, but this time there were three Playbills left over. So then he tried seven piles, but there were 4 Playbills left over. So he gave up and put them all back into the big box. He has fewer than 100 Playbills. How many Playbills does Lin have?make a list or chart would be helpful and explain your answer

Answer 1

Number of Playbills = P

First he arranged them all into four piles, but there was one Playbill left over. (n per pile)

P = 4n + 1

So then he tried five piles, but this time there were three Playbills left over. (m per pile)

P = 5m + 3

So then he tried seven piles, but there were 4 Playbills left over. (j per pile)

P = 7j + 4

4n + 1 = 5m + 3 ==> 4n = 5m + 3 -1 = 5m + 2

4n = 5m + 2

n = (5m + 2)/4

5m + 3 = 7j + 4

7j = 5m + 3 - 4 = 5m -1

j = (5m -1)/7

Making a table for different values of n, m and j that result in integers and keep P less than 100:

n = 13

m = 10

j = 7

P = 4(13) + 1 = 53

P = 5(10) + 3 = 53

P = 7(7) + 4 = 53

Answer:

Lin has 53 Playbills