# Algebraic Expressions & Equations

## Counting Down to Nationals

The countdown round is often the most anticipated and exciting part of competition for Mathletes^{®} and spectators alike. Here are some of our favorite countdown round problems from the 2019 competitions

__School #16__

On a certain farm, each chicken has two feet and each rabbit has four feet. If the combined number of chickens and rabbits on the farm is 100 and there are a total of 260 feet on these animals, how many chickens are there?

## Counting Down to Nationals

The countdown round is often the most anticipated and exciting part of competition for Mathletes^{®} and spectators alike. Here are some of our favorite countdown round problems from the 2019 competitions

** School #16**
On a certain farm, each chicken has two feet and each rabbit has four feet. If the combined number of chickens and rabbits on the farm is 100 and there are a total of 260 feet on these animals, how many chickens are there?

## Combining Shapes

The radius of circle N is 3 inches, and the radius of circle O is 4 inches. What is the radius of circle P whose area is the sum of the areas of circles N and O?

## It's Moving Day

Jessie and Marcus are moving from their apartment to a new condominium. Marcus is responsible for moving all his belongings and the living room furniture, while Jessie is responsible for moving all the kitchen items, including the dining table and chairs, and his personal belongings.

## Preparing for State

In just a few days, the 2019 MATHCOUNTS State Competitions will begin, so let’s look back at some of the 2018 State Sprint round problems and solve them in preparation.

## Space Junk

Space junk is debris orbiting Earth that, for the most part, has been abandoned or has broken off spacecrafts and rockets. Some of these items are far enough from Earth that they will remain in orbit forever; however, much of this “junk” will be pulled into Earth’s atmosphere by gravity. On average, one item per day falls victim to gravity. At this rate, in what year will 2500 pieces of space junk enter the atmosphere if we begin counting on February 18th?

## Time to Compete!

Chapter competitions officially start this week! Are you ready to compete? Perhaps solving these Sprint Round problems from the 2018 Chapter Competition will help you warm up.

__Sprint #15__

By switching two of the digits of the number 123,456, Rodrigo obtains a new number that is 1980 more than the original. What is the product of the two digits Rodrigo switched?

## Happy New Year!

Happy New Year! Now that 2019 is here, let’s have some fun solving this collection of problems that all involve the number 2019.

What is the greatest prime factor of 2019?

*The factors of 2019 are 1, 3, 673, 2019. The prime factors of 2019 are 3 and 673, the greatest being ***673***.*

## Best of 2018

As 2018 comes to an end, let’s go back and solve some of our favorite problems of year.

__School Handbook__

**Problem 237: **Kendra starts at a positive integer *k *and counts up by 4s until she hits exactly 200. Mason starts at a positive integer *m *and counts up by 6s until he hits exactly 200. If it takes Kendra half as many steps to reach 200 as it takes Mason, what is the greatest possible value of *k *− *m*?

## Sold Out

The Land O’ Lakes High School auditorium has exactly 26 rows of seats. The rows are labeled, in order, from the front of the auditorium to the back from A through Z. There are 8 seats in the row A. Each row after the first row has two more seats than the previous row. There are 10 seats in row B, 12 seats in row C and so on. How many seats are there in row Z?