## State Countdown

Here are a few of the problems that competitors had to solve as they faced off in head-to-head matches during the 2018 State 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.

## 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] *

## One for the Ages

Cara was born on January 1, 2010, and her mother, Sydney, was born on January 1, 1982. In what year will Sydney’s age be twice Cara’s age?

If we let Cara’s age be C, then Sydney’s age is S = C + 28, since Cara was born 28 years after Sydney. We are interested in determining when Sydney’s age is twice Cara’s age, in other words, when S = 2C. Substituting, we have C + 28 = 2C. Solving for C we get C = 28. Therefore, Sydney’s age will be twice Cara’s age in the year 2010 + 28 =.2038

## Three Little Piggy Banks

When Lucas dumped the coins out of his piggy bank, he noticed that there were only nickels and dimes, and the number of nickels was twice the number of dimes. If there were 50 nickels, what was the total value of the coins Lucas dumped out of his piggy bank?

## Autumn Leaves

The Wilsons traveled to Shenandoah National Park to view the fall foliage at its peak. The driving time from their home to the park was 2 hours. For the first third of the time they spent driving to the park, the Wilsons were in traffic and averaged 42 mi/h. During the second third of the two hours, they traveled at an average speed of 66 mi/h. For the final third of their trip, the Wilsons traveled on local mountain roads and drove an average of 30 mi/h. What is the total distance the Wilsons traveled to get to the park from their home?

## A Tasty Treat

Isabella went to the local ice cream shop with her three children, Christopher, Nina and Maria. Isabella and the kids each ordered a sundae with two scoops of ice cream and various toppings. A sundae with two scoops of ice cream costs $2.99, but the final cost of each sundae varies based on the number of toppings added. If the average cost, including sales tax, of the sundaes Isabella and her children ordered was $3.73, what was the total cost for all four sundaes?

## Bag of Bricks

Kaleb has a bag containing red, black and white LEGO^{®} bricks. If he has 12 more red bricks than white bricks and 15 fewer white bricks than black bricks, what is the positive difference between the number of red bricks and black bricks in Kaleb’s bag?

## School Makeover

Randolph has been contracted to tile classroom floors as part of the renovation of a local school. During the first five days on the job, Randolph completed tiling 4, 5, 6, 4 and 8 classrooms, respectively. What is the average number of classrooms Randolph tiled each day during that

five-day period? Express your answer as a decimal to the nearest tenth.