Counting Cookies

Santiago baked gingerbread cookies in the shapes of children. He gave each gingerbread boy and girl eyes made from chocolate covered candies in one of four different colors, a nose made from a butterscotch chip, toffee chip or peanut butter chip, and a mouth made from a piece of red licorice. Santiago then gave each gingerbread boy and girl buttons made from gum drops in one of four different flavors. For the final detail, he gave each gingerbread boy a blue bow tie, and each gingerbread girl a red hair bow.

Prime Number Sense

If n is the sum of three consecutive primes and is also the product of two 2-digit primes, what is the least possible value of n?

Let’s try the two 2-digit primes of least value, 11 and 13. These primes have a product of 143, and 143/3 is around 47. Two primes close in value to 47 are 43 and 53. So we try the sum 43 + 47 + 53 and see that it does, in fact, equal 143.

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?

Gobble! Gobble!

In 2018 the United States is expected to produce 240 million turkeys. That is a decrease of 1% compared to the number of turkeys produced in 2017. How many turkeys were produced in the U.S. during 2017? Express your answer to the nearest million.

Veterans Day

In celebration of Veterans Day, here are a few problems based on data obtained from the U.S. Census Bureau, 2017 American Community Survey 1-Year Estimates.

In the United States in 2017, there were an estimated 251,047,650 adult civilians (persons 18 years of age and older not currently enlisted in the U.S. military). If 18,204,605 of those individuals were veterans, what percentage of the adult civilian population of the United States did veterans account for in 2017? Express your answer to the nearest hundredth.

Voter Turnout

In the town of Newtonville, 60% of the registered voters turned out to cast their votes in the most recent election. If 2814 residents of Newtonville voted in this election, how many registered voters were there in Newtonville?

We are told that 2814 represents 60% of the registered voters in Newtonville. Thus, there are 2814 ÷ 0.60 = 4690 registered voters in Newtonville.

Fall Leaves

It’s Autumn, and that means leaves are falling! Amber’s house occupies 2650 ft2 in the middle of a 50-foot by 80-foot parcel of land, and the leaves that fall cover the ground all around her house. If it takes Amber’s family 4.5 hours to rake all the leaves, how many square feet of leaves did they rake each hour?

Columbus Day

Christopher Columbus landed in the Americas accidentally. He was actually trying to find a faster trade route to Asia from Spain. Instead of sailing around the tip of Africa, Columbus believed he could sail west across the Atlantic Ocean to reach Asia. In planning his expedition, Columbus calculated the journey would be around 2300 miles, based on his estimation of the earth’s size. Nautical experts of the time disagreed with his calculations, estimating the distance would be closer to 12,200 miles.

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.