Lower Elementary:
Question: Tracie placed 20 ornaments on the Christmas tree. Anna placed 5 more ornaments on the Christmas tree than Tracie. Patty placed twice as many ornaments on the Christmas tree than Anna. How many ornaments did Patty place on the Christmas tree?
Answer: 50 ornaments
Solution: In order to find out how many ornaments Patty put on the tree, we need to first know how many ornaments Anna put on the tree. Anna put on 5 more ornaments on the Christmas tree than Tracie. Tracie put 20 ornaments on the tree, so Anna put 25 ornaments on the tree (20 + 5 = 25). Patty put twice as many ornaments on the tree than Anna. 25 doubled is 50. Patty put 50 ornaments on the tree.
Upper Elementary:
Question: A Christmas tree is on sale for $6.00 a foot. Charlie buys a 5½ foot tree. If he pays $40, how much change would Charlie get back?
Answer: $7
Solution: First we need to find the cost of the tree. The tree costs $6.00 a foot, and Charlie buys a 5½ foot tree. So, the tree costs $33.00 (6 × 5½ = 6 × 5 + 6 × ½ = 30 + 3 = 33). Since Charlie pays $40, he would receive $7 in change (40 – 33 = 7).
Middle School:
Question: Tim, Martin, and Eileen went to a white elephant Christmas party. They each received a stuffed animal from the party: one received a stuffed cat, one received a stuffed dolphin, and one received a stuffed panda. The gifts were in different colored boxes: one was in a blue box, one was in a green box, and one was in a red box. The red box was the one that contained the panda. Eileen received the cat, but it was not in the blue box. Tim did not receive the dolphin. What animal did Martin receive and in what color box?
Answer: The dolphin in the blue box
Solution: There are 3 people, 3 colored boxes, and 3 stuffed animals. We know the red box contained the panda. Eileen received the cat, but not in the blue box. This means that Eileen did not get the red box, since the red box contained the panda and she received the cat. Since Eileen did not receive the red box or the blue box, that means she must have received the green box. So, Eileen received the cat in the green box, and the panda is in the red box. Since Eileen has the cat, Tim can’t have the cat. And since Tim did not receive the dolphin either, that means that Tim must have the panda in the red box. So Eileen received the cat in the green box and Tim received the panda in the red box. That means that Martin must have the dolphin in the blue box.
Algebra and Up:
Question: A group of 6 friends decide to do a secret Santa. Each person writes their name on a piece of paper and puts it in a hat. Each person then takes turns to draw a random name from the hat and keeps the piece of paper. What is the probability that the first person gets the second person, the second person gets the third person, the third person gets the fourth person, the fourth person gets the fifth person, the fifth person gets the sixth person, and the sixth person gets the first person?
Answer: 1/720
Solution: There are 6 names in the hat when the first person draws a name, so there is a 1/6 probability of the first person to draw the second person’s name. Now there are 5 names left, so the second person has a 1/5 probability of drawing the third person’s name. Now there are 4 names left, so the third person has a 1/4 probability of drawing the fourth person’s name. Now there are 3 names left, so the fourth person has a 1/3 probability of drawing the fifth person’s name. Now there are 2 names left, so the fifth person has a 1/2 probability of drawing the sixth person’s name. Since there is only one name left in the hat, and that person has to be the first person’s name, there is a 1/1 probability of the sixth person drawing the first person’s name. To find the probability, multiply each of the probabilities together. 1/6 × 1/5 × 1/4 × 1/3 × 1/2 × 1/1 = 1/720.
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