Problem Solving (Misc.)
Today is 11/13/17, which makes it a “prime time” to solve the following problems involving prime numbers!
For each of the prime numbers less than 30, Wallace writes down all the number’s positive factors. What is the sum of all the numbers Wallace writes down?
Due to timekeeping confusion on the American railroads in the mid-19th century, a system of standard time zones was proposed. In 1918 the Standard Zone Time and Daylight Saving Time were established in the Standard Time Act. Later, the Uniform Time Act of 1966 was passed promoting the adoption of uniform time within the standard time zones. The map below shows six of the U.S. time zones.
The letters of the words GHOST, GHOUL, TRICK, TREAT and CANDY were written on 25 index cards, one letter per card. If the cards are shuffled and one card is selected at random, what is the probability that the card contains one of the letters in the word GHOST? Express your answer as a common fraction.
When Lucas dumped the coins out of his piggy bank, he noticed that there were only nickels and dimes, and the number of nickels was twice the number of dimes. If there were 50 nickels, what was the total value of the coins Lucas dumped out of his piggy bank?
The Wilsons traveled to Shenandoah National Park to view the fall foliage at its peak. The driving time from their home to the park was 2 hours. For the first third of the time they spent driving to the park, the Wilsons were in traffic and averaged 42 mi/h. During the second third of the two hours, they traveled at an average speed of 66 mi/h. For the final third of their trip, the Wilsons traveled on local mountain roads and drove an average of 30 mi/h. What is the total distance the Wilsons traveled to get to the park from their home?
Isabella went to the local ice cream shop with her three children, Christopher, Nina and Maria. Isabella and the kids each ordered a sundae with two scoops of ice cream and various toppings. A sundae with two scoops of ice cream costs $2.99, but the final cost of each sundae varies based on the number of toppings added. If the average cost, including sales tax, of the sundaes Isabella and her children ordered was $3.73, what was the total cost for all four sundaes?
Mrs. Marble refers to the three students named Ashley in her 3rd period gym class as Ashley G., Ashley E. and Ashley V. Mrs. Marble needs to divide the class to make 6 teams of 5 players for the dodge ball tournament. Each student has been assigned a number from 1 to 30. Mrs. Marble has placed 30 cards, each containing a number from 1 to 30, in a bowl. She will randomly select groups of 5 cards, without replacement to make the teams. What is the probability that all three Ashleys will be on the same team? Express your answer as a common fraction.