Problems of the Week – January 1 to January 5

Click here ^[1] for the Problem Extension Worksheet version of the Problems of the Week.
Click here ^[2] for an MS Word version of the Problems of the Week.
Click here ^[3] for the Canadian Problem Extension Worksheet version of the Problems of the Week.
Click here ^[4] for a Canadian MS Word version of the Problems of the Week.

^[5]Lower Elementary:
Question: James has a New Year’s resolution to be able to run a mile without stopping. If he can run one quarter of a mile without stopping by the end of January and he adds another quarter of a mile every month, then by the end of which month will James be able to run the full mile without stopping?
Answer: April
Solution: There are 4 quarters in a whole, so it’ll take 4 months—January, February, March, and April—for James to be able to run a whole mile without stopping. James will be able to run the full mile by the end of April.

^[6]Upper Elementary:
Question: Barb’s New Year’s resolution is to build her vocabulary. She plans to learn 3 new words in January, 6 new words in February, 12 new words in March, 24 new words in April, and so on. If the pattern continues, then how many new words are on Barb’s 2018 vocabulary list in total?
Answer: 12,285 words
Solution: Each month, Barb learns twice as many vocabulary words as she did the previous month. So, Barb will learn 24 × 2 = 48 words in May, 48 × 2 = 96 in June, 96 × 2 = 192 in July, 192 × 2 = 384 in August, 384 × 2 = 768 in September, 768 × 2 = 1,536 in October, 1,536 × 2 = 3,072 in November, and 3,072 × 2 = 6,144 in December. If we add them all up, we get 12,285 words in total.

^[7]Middle School:
Question: Daniel’s New Year’s resolution is to visit the library more often. He will consider his resolution successful if he goes to the library on 40% of the days in 2018. How many days need to include library visits for Daniel’s resolution to be successful?
Answer: 146 days
Solution: 2018 is not a Leap Year, so there will be 365 days. For Daniel to visit the library on 40% of those days, he will need to visit the library on 365 × 0.4 = 146 days.

^[8]Algebra and Up:
Question: Sally has a New Year’s resolution to practice playing her violin for more than three hours per week. She won’t practice for more than one hour per day. Write a compound inequality that represents the amount of time Sally will practice playing the violin per week.
Answer: 3 < x ≤ 7
Solution: Since the number of hours Sally practices is more than 3, we can write that part of the inequality 3 < x. We use the < symbol because 3 isn't a possible value. Another way to say that Sally won’t play more than more than an hour per day (7 hours per week) is to say that Sally will play less than or equal to 7 hours: x ≤ 7. To write this as a compound inequality, all we need to do is stick our two inequalities together: 3 < x ≤ 7.