Students in a painting class must pay an extra art supplies fee. On the first day of class, the instructor collected $28 in fees from several students. On the second day she collected $21 more from some different students, and on the third day she collected an additional $63 from some other students.
a.) What is the most art supplies fee could cost a student?
b.) Determine how many students paid the art supplies fee each day.
Please explain how you go the answer.
Remark You need to assume that the fee is a whole number. It's not stated, but it really should be. That makes your life so much easier if you make that assumption.
Step One Factor each of the 3 amounts into their common prime factors.
28 = 2 * 2 * 7 21 = 3 * 7 63 = 3 * 3 * 7
Step Two Pick out the factor that is common to all three amounts. You can see that it is 7. Each student had to pay 7 dollars in art fees.
Step Three Find the number associated with the amount that is not a 7. 28 dollars has a 4 along with the 7. 4 students paid on the first day 21 dollars has a 3 along with the 7. 3 students paid on the second day 63 dollars has a 9 along with the 7. 9 students paid on the third day.
So the class size was 4 + 3 + 9 = 16 students in the class, or at least there were 16 paying students in the class.
