# Problem Solving (Misc.)

## Martin Luther King, Jr. Day

Dr. Martin Luther King, Jr., a civil rights activist whose passion and leadership led to great cultural changes in America, was born on January 15, 1929. On November 2, 1983, President Ronald Reagan signed a bill to create a federal holiday honoring Dr. King. The national holiday celebrating the birth of Dr. King was first observed on January 20, 1986. Every year since, Martin Luther King, Jr. Day has been observed on the third Monday of January.

What is the earliest date in January that Martin Luther King, Jr. Day can occur?

## Shaping Up

Jayden started a new exercise program that includes running, cycling, yoga and aerobics. The chart shows how many calories Jayden burns by doing these exercises. Use this data to answer the questions that follow.

## Gift Exchange

Sam, Pam, Ken and Jen are exchanging gifts for the holiday. Each name is written on a slip of paper and placed in a bowl. Sam is the first to randomly select a name from the bowl. What is the probability that Sam selects his own name? Express your answer as a common fraction.

## Geometry of Gift Giving

Vanessa bought some round holiday dessert plates to give as a gift to her friend. However, the store only had 5 of the 8 plates she wanted. (All of the plates are the same.) The stack of five plates measured 1.5 inches tall, and when two plates were removed from the stack the remaining stack of three plates had a height of 1 inch. When Vanessa finally has all 8 of the plates she wants, how tall will the stack of 8 plates be, in inches? Express your answer as a decimal to the nearest hundredth.

## 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.