Are you smarter than a 3rd grader? John has 8 quarters. He buys a bottle of pop and gets 6 dimes in change. How much does the pop cost?
Surprising answer waaaay down below.
At Mathnasium (in the United State), we love quarters. Most of our new students know it's money. A few have never heard of it. We always ask, “How many quarters are there in a dollar?” If we get “four!”, then we’re happy. Now we have a chance to explain why 25 cents is called a quarter. We’ll likely explain that the root word of quarter is the Latin “quattor” or fourth. Since a dollar is 100 cents, and 25 cents is a quarter of 100, calling 25 cents a quarter makes sense; and just to belabor the point, 4-quarters make a 100 cents.
When we arrived in the US, quarters confused us. We were used to larger coins in  1⁄5 denominations (20 cents) as is commonly used outside the United States. We commiserate when we see new students who come from other countries. Rather than simple units of 10s, that extra 5 cents in a quarter makes for awkward calculations. In the US, the choice of  1⁄4 as a denomination originated in 1796 with the practice of dividing Spanish milled dollars into eight wedge-shaped segments. "Two bits" (that is, two "pieces of eight") is a common nickname for a quarter. Fan of the Pirates of the Caribbean should be familiar with the phrase “pieces of eight” (squawk! -- imagine the parrot).
Did you get 15 cents?
No? Then hopefully you got $1.40. If you did, then your reasoning was, 8 quarters is 2 sets of 4-quarters, each set of 4 being $1.00, so 2 sets is $2.00. 6 dimes is 60 cents. So, our change can be found by counting up from 60 to 100 = 40, and 100 to 200 = 100, or a total of $1.40.
More critically, why was the change 6 dimes? That can result from the least number of quarters used. 3 quarters = 75 cents. So, 75 cents – 60 cents = 15 cents. In this case, John could have used a single quarter and received 10 cents back. Perhaps John wanted the extra dimes for other purposes.
Of course, it’s possible that John is a foreigner, unfamiliar with US coinage, and decided to hand over excess change to cover his purchase. Notice that the question does not specify how many quarters John exchanged for the pop. Assuming an honest merchant, then the pop could cost a minimum of 15 cents for 3 quarters of change, or 40 cents for 4-quarters, 65 cents for 5-quarters, etc up to a maximum of $1.40 for all 8-quarters of change.
How many of you have done that in a foreign country, given a large bill for a small purchase, and nonchalantly fumbling the change? We’ve been there!
Contact:
Ruby Yao and Benedict Zoe, Mathnasium of Fort Lee
201-969-6284 (WOW-MATH), [email protected]
246 Main St. #A
Fort Lee, NJ 07024
Happily serving communities of Cliffside Park, Edgewater, Fort Lee, Leonia, Palisades Park, North Bergen, West New York, and Fairview.
(201) 461-6284
(201) 969-6284
