Final Countdown

On Sunday, May 13th, 224 middle-school math students participated in the written rounds of the 2018 Raytheon MATHCOUNTS National Competition. On Monday, May 14th, the top 12 competitors will go head to head in the National Countdown Round to determine the 2018 MATHCOUNTS National Champion. Let’s solve a few problems from the 2017 National Countdown Round.

Congrats, State Winners!


Congratulations to everyone who competed in the 2018 State Competition, especially to the winners who are headed to Washington, DC next month to compete in the 2018 Raytheon MATHCOUNTS National Competition! Now that the competitions have officially wrapped up, let’s take a look at a few of the challenging problems from the 2018 State Competition.

A Look Back at Chapter


This week, the 2018 State Competitions will wrap up, and 224 state competitors will begin preparing to compete at the Raytheon MATHCOUNTS National Competition. Let’s take a look back at a few of the chapter problems they encountered on their way to state.

Get Ready for State


This month the 2018 MATHCOUNTS State Competitions will take place, so let’s look back at some of the 2017 State Sprint round problems and solve them in preparation.

Andre can complete 5/6 of a job in 3/4 of the time that it takes Michael to do the whole job. What is the ratio of the rate at which Andre works to the rate at which Michael works? Express your answer as a common fraction.

Let the Competitions Begin!

Chapter competitions officially start this week! Are you ready to compete? Let’s try a few 2017 Chapter Competition problems to get warmed up.

If the sum of the positive integer a and 5 is less than 12, what is the sum of all possible values of a?

[Sprint #16]     

Baking Fruit Cake

Allie plans to make a fruit cake for her family plus four more to give away to friends. Shown here is a list of the ingredients required to make a fruit cake according to Allie’s recipe. How many ounces of mixed fruit are needed for Allie to make five fruit cakes, according to her recipe?

fruit cake ingredients.eps

O, Christmas Tree

Although, Franklin Pierce, the 14th U.S. President, originally brought the Christmas tree tradition to the White House, it was Calvin Coolidge, the 30th U.S. President, who, in 1923, started the National Christmas Tree Lighting Ceremony now held every year on the White House lawn. Last week, the president and first family continued that tradition by lighting a tree on the White House lawn. And speaking of trees, try to solve the following Christmas tree-themed problems.


Mrs. Hillestad has planned a dinner for 15 people this Thanksgiving. She bought 22.5 lbs of turkey, plus potatoes, cranberry salad, rolls and all of the traditional holiday food. Unfortunately, her daughter forgot to tell her that she was bringing three of her friends.  If Mrs. Hillestad wants to feed each person the same amount of turkey that she had originally planned, how much additional turkey must she purchase to accommodate these additional guests? Express your answer as a decimal to the nearest tenth.

Apples, Apples and More Apples!

The Farmers Market sells apples by the bushel, and each bushel of apples weighs 42 pounds. A bushel of large apples contains 84 apples. If a bushel of small apples contains twice as many apples as a bushel of large apples, how many small apples are in 1 pound of apples?