A school keeps track of the percentage of scholars who pack lunch versus buy lunch. On Monday, 80% of scholars packed lunch. On Tuesday, 70% of the scholars who packed lunch do so again, and 50% of those who bought lunch on Monday pack lunch on Tuesday. Assume all scholars either pack lunch or buy lunch. Find the percent change in the number of scholars who bought lunch from Monday to Tuesday, and indicate whether this was an increase or decrease.
Let's assume there are 100 scholars in total.
On Monday, 80% of scholars packed lunch, which means 80 scholars packed lunch and 20 scholars bought lunch.
On Tuesday, 70% of the scholars who packed lunch on Monday packed lunch again, which means 0.7 * 80 = <<0.7*80=56>>56 scholars packed lunch.
On Tuesday, 50% of the scholars who bought lunch on Monday packed lunch, which means 0.5 * 20 = <<0.5*20=10>>10 scholars packed lunch.
Therefore, on Tuesday, a total of 56 + 10 = <<56+10=66>>66 scholars packed lunch.
The number of scholars who bought lunch on Tuesday is 100 (total scholars) - 66 (scholars who packed lunch on Tuesday) = <<100-66=34>>34 scholars.
The percent change in the number of scholars who bought lunch from Monday to Tuesday is (34 - 20) / 20 * 100% = 14 / 20 * 100% = 70%.
Thus, there is a 70% increase in the number of scholars who bought lunch from Monday to Tuesday.