# Problem Solving (Misc.)

## Gourmet Candies

Sugar Shack gourmet candy shop’s signature candy mixture contains Sour Drops, Chocolate Chews and Tangy Twists in the ratio 2:3:4, respectively. How many more pounds of Tangy Twists than Sour Drops are in a 45-pound batch of this signature candy mixture?

## Hot Air Balloons

Fall is a beautiful time of year to take a hot air balloon ride! You may not be able to take a balloon ride, but we hope you enjoy solving this week’s problems.

Melrose’s hot air balloon is a sphere of diameter 100 feet. How many cubic feet of air will Melrose’s hot air balloon hold when completely filled? Express your answer as a decimal to the nearest tenth.

## What's for Lunch?

Each week, Devin buys school lunch on Friday because the cafeteria serves pizza every Friday. Monday through Thursday, Devin brings his lunch to school. The lunch he brings always includes a peanut butter and jelly sandwich, a fruit and a drink. Devin has enough fruit and drink options to make a different lunch every day that he brings lunch for the next four weeks. If Devin has the same number of fruit options as he has drink options and he takes no days off from school, how many different fruit options does he have?

## Asteroid Blaster

In the video arcade game Asteroid Blaster there are a total of five rounds on the first level. During each round, asteroids appear on the screen and players must blast as many as possible before time expires. To advance to the next round, a player must destroy all the asteroids in the current round. This becomes more difficult to accomplish because the number of asteroids increases with each round. Rounds 1, 2 and 3 each have 1, 8 and 27 asteroids, respectively. If this pattern continues, how many asteroids will there be to destroy in Round 4?

## Math Club Meetings

Ms. Cross leads The National Math Club at the middle school where she teaches. At the first club meeting of the school year, 60% of the students in attendance were boys. If there was one fewer girl than boy in attendance, how many students attended the first club meeting?

## Happy New (School) Year!

A new school year often means new school clothes, new teachers and new friends. One of our favorite parts of a new school year is the release of a new *MATHCOUNTS School Handbook*! Download your free copy after solving a few problems from some previous handbooks.

Lily is going to the movies with Abby, Bea and Jaclyn. Abby wants to sit at the end of a row, and Bea only cares that she is seated next to Jaclyn. In how many different ways can the girls be seated in a single row that has only four seats?

## New School Clothes

Nona went shopping to buy some new school clothes. At the first store she bought two pairs of pants, each originally priced $30. Nona used a coupon that reduced the price of each item by 15%, and then a 5% sales tax was applied to the new subtotal. What was the total purchase price?

## Happy Left Handers Day!

International Left Handers Day is celebrated each year in August. If the ratio of the number of days of the month before International Left Handers Day to the number of days of the month after it is 2:3, on what date in August is this special day observed?

## 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*?