Can You Solve This Math Problem?

Hi, Jennifer.

My son was given the following question on a practice SAT exam this morning: “On the last day of a one-week sale, customers numbered 149 through 201 were waited on. How many customers were waited on that day?”

What is the correct answer to this problem, and why?
– Stumped Mama

Dear Mama:

If customer #149 and #201 and everybody in between were waited upon, that would total 53 people. Think about it this way: If ten people are waiting in line at Andy’s for frozen custard and numbers 1 through 10 are served, that isn’t just 9 customers (1+9=10), it’s actually 10 customers, because you count the first customer, too. They serve him, plus the nine people after him. Expand that to your problem. 149 + 52 = 201, but if they are serving #149, also, that would be a total of 53 customers who are waited upon: #149, plus the 52 people in line behind him. You have to count both endpoints. Doesn’t that make sense?

Tell your son not to get discouraged. That kind of question trips up a lot of students, but once you know the trick, it’s easy!
Jennifer