Solve. Use algebraic reasoning to explain your solution.
Dad bakes some cookies. He eats one hot out of the oven and leaves the rest on the counter to cool. He goes outside to read. Dave comes into the kitchen and finds the cookies. Since he is hungry, he eats half a dozen of them. Then Kate wanders by, feeling rather hungry as well. She eats half as many as Dave did. Jim and Eileen walk through next, and each of them eats one third of the remaining cookies. Hollis comes into the kitchen and eats half of the cookies that are left on the counter. Last of all, Mom eats just one cookie. Dad comes back inside, ready to pig out. “Hey!” he exclaims. “There is only one cookie left!” How many cookies did Dad bake in all?
Mr. Peanut has a tendigit telephone number (including the area code) in which each digit, 0 through 9, appears once. The first digit on the left is divisible by 1, the first two digits form a number divisible by 2, the first three digits form a number divisible by 3, the first four digits form a number divisible by 4, and so on, until we get to the whole 10digit number which is divisible by 10. What is Mr. Peanut's phone number?
Hint: Make a chart with 10 blank spaces. Use what you know about divisibility rules to decide which numbers can go in each blank. Then, try to find all the possible combinations. Remember, each digit (09) must be used ONLY once. Post your reasoning in the comments below. The zoo has a train that carries people between exhibits. One morning the first
passengers got on at Monkey House. At Alligator Pond, the number of people who got on was 3 more than got on at Monkey House. The train made 4 more stops at Tiger Thicket, Panda Playground, Giraffe Savannah, and Big Cats. At each of these stops, 3 more passengers boarded the train than at the previous stop. At Big Cats, 20 people got on the train. How many passengers in all boarded the train? Answer using the comments section below. Be sure to explain your thinking. Do you really have time for school? I'll prove that you do not!
"There are 365 days in a year. Let's assume that you sleep 10 hours each day. This means that, in one year, you are asleep for 3650 hours, which is equivalent to 152 full days (3650 hours divided by 24 hours per day). 365  152 = 213 (days you have left in the year) We all know school is not open on weekends, so you can't go to school then. There are 104 Saturdays and Sundays in a year (52 weeks x 2 days in a weekend). 213  104 = 109 (days you now have left) And school is not open during summer vacation. Summer vacation is at least 2 full months, so that's another 60 days you aren't in school. 109  60 = 49 (days left) And you have to eat every day and have a little time to relax and play. Let's say that takes around 3 hours each day. That is 45 days worth of hours (365 days x 3 hours each day to relax = 1095 hours. Divide by 24 hours in a day to get 45 days). 49  45 = 4 (days left now) I haven't even counted holidays, and there's at least 4 of them during the year. So that leaves you with zero days left to go to school!" What is wrong with this explanation? How do you have time to be at school? Hint: All the math is correct. Post your reasoning using the comments button below. A new problem of the week will be posted each weekend along with an explanation of the previous week's problem. Discuss your solution by posting comments.
Ground rules for comments:

Problem of the WeekNew problems posted each weekend. Discuss using comments. Archives
February 2016
