Question. There are 90 students who have lunch during period 5. Today, two-thirds of the students sat in the cafeteria, while the remainder sat at the covered picnic tables outside. But some yellow-jackets were attracted to their food, and so one-third of the students outside jumped up and ran inside to the cafeteria, while 3 of the students in the cafeteria went outside to see what all the fuss was about. How many students are now in the cafeteria?
Answer. 67
What step-by-step reasoning justifies that answer?
Reasoning: Originally, there were 90 * 2 / 3 = 60 in the cafeteria. Originally, there were 90 - 60 = 30 outside the cafeteria. Then 30 * 1 / 3 = 10 ran inside. The number of students inside the cafeteria grew by 10 - 3 = 7. There are now 60 + 7 = 67 students in the cafeteria.