# Problem Solving (Misc.)

## In Sequence

What is the 20th term of the arithmetic sequence 13, 19, 25, 31, ...?

*The common difference is 19 – 13 = 6. Now that we know that we can find the 20th term by 13 + 6(20 – 1). Thus, the 20th term is **127**.*

What is the sum of A and B in the arithmetic sequence 7, 15, 23, A, 39, B, ...?

## Summer Camp

Summer Fun Camp enrollment costs 85 dollars each week per camper. Each camper may register for up to three of the optional workshops offered for an additional charge of $5.50 a week per workshop, or 15 dollars per week for three workshops. The total charge for Chloe’s enrollment to attend Summer Fun Camp for *n* weeks this summer is 768 dollars. If Chloe has registered to participate in two workshops each week, what is the value of *n*?

## Making Sense of Numbers

Here are a few problems to keep your number sense sharp during the summer months.

What is the greatest positive three-digit integer that is divisible by 5, 7 and 9?

*We know that any three-digit number that is divisible by 5, 7 and 9, is divisible by 5 × 7 × 9 = 315. The largest three-digit multiple of 315 is 315 × 3 = 945.*

## Moving Day

The summer months are the most popular time to move to a new home. Janet’s family is moving, and she suddenly realizes just how much stuff they have in their current home. Once the moving company finishes packing everything in boxes, they begin the task of numbering them. A sticker is placed on every box and on every item that is too large to fit in a box. Janet notices that stickers in three distinct colors are used. There are blue stickers numbered 239 through 262, green stickers numbered 163 through 178 and yellow stickers numbered 453 through 492.

## In the Shade

A tree shades part of a rectangular table, as shown, so that two seats are in the sun and two are in the shade. Will, Xavier, Yvette and Zoe are in search of a place to sit and enjoy their lunches. If Yvette insists on sitting in the shade, and Zoe refuses to sit next to Will, how many different arrangements are there for Will, Xavier, Yvette and Zoe to be seated at this table?

## Archer's Three Sons

Archer has three sons named Tanner, Carver and Decker. Archer’s age is three times the sum of Carver’s and Decker’s ages. The sum of Tanner’s and Carver’s ages is half Archer’s age. If Tanner’s age is three times Carver’s age, what is the ratio of the ages of Carver and Decker? Express your answer as a common fraction.

## Family Vacation

The summer has unofficially begun for many families around the country, so here are a few problems related to Miranda’s family vacation.

When packing for the trip Miranda didn’t want to bring a lot of extra clothes, so she packed 4 shirts, 2 pairs of shorts and 1 skirt (all of which coordinate). If an outfit consists of a shirt and a pair of shorts or a skirt, how many distinct outfits did Miranda pack?

## Let the Games Begin!

This season, each team in the Davis City softball league will play each other team exactly once. If a total of 15 games will be played, how many teams are in the league?

## 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.

## Mathopolis Snowfall

The snowfall in Mathopolis totaled 68.1 inches in 2015 and 11.2 inches in 2017. If the average yearly snowfall for 2015, 2016 and 2017 was 35.6 inches, how many total inches of snow fell in Mathopolis in 2016? Express your answer as a decimal to the nearest tenth.