Problem Solving (Misc.)
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?
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?
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?
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?
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?
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 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?
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.
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.
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?