Winter Break Problem Solving Challenge! Due: January 5
Directions: Choose 5 problems to solve. Show all work on attached lined paper. This will be graded as a quiz grade for the 3rd quarter.
- Cyndi lives on a farm. Her family raises cows and chickens. One day Cyndi counted how many total legs there were on all of the cows and chickens (assume that all of the cows have 4 legs and all of the chickens have 2 legs). She counted 78 legs. If the total number of cows and chickens is 25, then how many cows live on Cyndi’s farm?
- Sylvester measured his pulse and found that his heart beats at a rate of 80 beats per minute. At this rate, how many days will it take his heart to beat 1,000,000 times?
- How many minutes did Heidi, Saul, and Joy each travel to get to the skating rink on Saturday? Joy came by skateboard, Heidi came by bike, and Saul came on the bus. It took Heidi twice as long as Joy to get there. It took Saul 10 minutes more than it took both the girls together. All three skaters together took 64 minutes to get to the rink.
- At Tri-City Middle School, half of the 470 students are taking algebra. One-fifth of the students not taking algebra are taking geometry, and each of the remaining students is taking pre-algebra. How many students enrolled at Tri-City Middle School are taking pre-algebra?
- The duration of a ride on the Shocker roller coaster is 1minute 30 seconds. The Shocker has only one train consisting of a series of linked cars, each of which carries apair of passengers. It takes each group of passengers exactly 30seconds to board the train and exactly 30 seconds to exit the train. In one hour 480people board the train, complete the ride and exit the train. Assuming there is never a seat left vacant, how many linked cars are in the Shocker’s train?
- Your family won the lottery and you have so much money that you decide to give away 2.5 million dollars ($2,500,000). If you give away $50 every hour, how long will it take you (to the nearest tenth of a year) to give away the 2.5 million dollars?
- Four friends ran a race. Matt finished 7 seconds ahead of Ziggy. Bailey finished 3 seconds behind Sam. Ziggy finished 5 seconds behind Bailey. In what order did the friends finish the race?
- Triskaidekaphobia is an irrational fear of the number 13. Because of fear and superstition surrounding the number 13, it is common in tall buildings for the 13th floor to be skipped when installing elevators buttons, it is instead numbered 14. A particularly fearful hotel owner decided to skip floor 13, as well as, any multiples of 13 when numbering the floors. He did the same thing when numbering the rooms. If each floor has rooms numbered to 100 and the elevator has buttons numbered to 30, how many rooms does the hotel have?
- A relay team consisting of four runners – Anne, Bryn, Carmen and Dahlia – completed a race in 72 minutes. Anne’s leg of the race took 1/5 of the total time; Bryn’s took 1/3 of the total time; and Carmen’s took 3/10 of the total time. How many minutes did Dahlia take to run her leg of the race?