Ms. Carmona Saturday sessions Problem Solving Ms. Carmona Saturday sessions

Problem Solving Bus Stop At the end of the day there are 100 people on the bus, and all are headed home. At each bus stop exactly 3 people get off the bus, and nobody gets on the bus. How many people are on the bus after the 19th bus stop? after the nth bus stop?

Problem Solving Sequences The numbers in the sequence 2, 7, 12, 17, 22, … increase by fives. The numbers in the sequence 3, 10, 17, 24, 31, … increase by sevens. The number 17 occurs in both sequences. If the two sequences are continued, what is the next number that will be seen in both sequences?

A Bear of a Problem Last summer we went camping in Yosemite, and the first night we did a dumb thing: we left out food on the ground. A bear came along and ripped up one-third of our total number of dried meals. The next day we ate four of the remaining meals and tied the food up in a tree. It didn’t seem to help because one-third of the meals we had left were ripped open by another bear. During our third day, we ate four more meals and that night, despite everything we did, one-half of our remaining dried meals were ripped apart. We gave up, ate the four remaining dried meals, and headed home. Can you tell how many dried meals we started with?

Horse Selling “I want to sell my horse. You see- a while back I bought him for $50.00. Then, I sold him to a friend for $60.00. Afterwards, I bought him again for $70.00, and now my friend offers me $80.00. If I sell the horse back, am I going to win or lose money in these transactions?”

Big Long Lake The surface of Big Lake is 31 feet above the surface of Long Lake. Long Lake is half as deep as Big Lake and the bottom of Long Lake is 8 feet below the bottom of Big Lake. How deep is each lake?

The Six Story Building A six-story building has stairs between equally spaced floors. How many times higher is the climb from the first to the sixth floor than the first to the third floor?

The Striking Clock A clock takes 12 seconds to strike 12 times at 12 o’clock. How long does it take to strike 6 times at 6 o’clock?

Hand Shakes If there were 20 people at a party. If each person shakes hands with each other person, how many handshakes will there be?

Hidden Beads How many beads are hidden behind the cloud? Figure not drawn to scale.

Triangle Sums Arrange the digits 1, 2, 3, …, 9 in the triangle so that each side sums to 20.

Boxes of fruit Three boxes each contain fruit. One box only contains apples, one box only contains oranges, and the third box only contains a mixture of apples and oranges. All boxes are mislabeled. By selecting one fruit from one of the boxes, can you correctly label the three boxes? Why or why not?

A Rich Estate Mr. Phil T. Rich left half of his estate to his wife, $30,000 to his daughter, half of what was left to her butler, half of what remained for the care of his goldfish, and the remaining $8,000 to charity. What was the value of the estate?