Practice Problems December 2004

7P-16) Pablo spent the entire day on the roller coaster at Four Flags Amusement Park. As he finally left the park, just before closing time, he saw a huge, lime-green dinosaur at the Ring-Toss Booth. He knew it would be the perfect birthday present for his little sister. "Wait a minute," he said to his friends, "I have to win this for Oriana." His friends watched as Pablo was given four rings to toss. He aimed each ring at six pins labeled 25, 20,10, 8, 5, and 0. The person in the booth explained, "You must toss all four rings, and your total must be 40 points to take the prize dinosaur." How many different ways could Pablo toss the rings and win the dinosaur? Explain in detail how you found your answer using words, numbers, and/or pictures.

7P-15) The Clinton School is putting numbers on the new basketball jerseys. Players must choose two numbers from the set of 1, 3, 5, 7 and 9. How many different two-digit numerals can they make? What if they might also select a one-digit numeral? Explain in detail how you found your answer using words, numbers, and/or pictures.

7P-14) The Continental Hockey League consists of two conferences, each with six teams. Every team plays the teams within its own conference twice and plays each team in the other conference once. How many games are played during the season? Explain in detail how you found your answer using words, numbers, and/or pictures.

7P-12) It's Party Day at the zoo. Gina and her friends each have three tickets, so they are trying to decide what three activities they want to do. They could enter a costume contest, watch a monkey show, go through a hunted house, watch a play, or go on a hay ride. How many different combinations of three activities they could choose? Explain in detail how you found your answer using words, numbers, and/or pictures.

7P-11) It's true: The odds of finding a cracked egg in a shipment of eggs is 1 egg in 24 cartons before those cartons are placed on grocery store shelves. Once they are on shelves, however, your odds of getting a cracked egg rise to 1 egg in every 10 cartons. Each carton holds a dozen eggs. How many cracked eggs can a grocery expect to find a shipment of 2,880 eggs just off the truck? How many more of these eggs will be cracked after being put on shelves? About what percent of the total shipment of eggs will be broken? Explain in detail how you found your answer using words, numbers, and/or pictures.

7P-10) Nick and Jenny are playing a game. There are six tiles in a box: three red and three blue. A player picks two tiles without looking. Jenny gets a point if the tiles don't match; Nick gets a point if they do match. What are the odds that both tiles will have the same color? Is this a fair game? Explain in detail how you found your answer using words, numbers, and/or pictures.

7P-5) What are the odds that flipping a coin will result in heads? What are the odds that two students, each flipping a coin, will both get head? What are the odds that three students, each flipping a coin, will all get heads? What are the odds that four students, each flipping a coin, will get heads? Will you ever reach the point where it is impossible for a group of students, each flipping a coin, to get head? Explain in detail how you found your answer using words, numbers, and/or pictures.

6P-17) There are five slices of pizza in a box: 2 pepperoni, 1 mushroom, and 2 eggplant. If you reach into the box without looking and take a slice, what is the probability you will get a pepperoni slice? Explain in detail how you found your answer using words, numbers, and/or pictures.

6P-16) A high school senior was packing for his trip abroad. He packed 4 different shirts, 3 different pairs of pants, and 3 different sweaters. He plans to wear a shirt, pair of pants, and sweater each day. How many different outfits are possible? Explain in detail how you found your answer using words, numbers, and/or pictures.

6P-13) How many different ways can you arrange four books on a shelf? Explain in detail how you found your answer using words, numbers, and/or pictures.

6P-9) There is a game at the County Fair in which five balls are placed into a basket. Each ball has a number printed on it: 0, 2, 4, 6, 7. A person picks three of the balls from the basket at one time and adds the numbers. 1. How many different sums are possible? 2. What is the probability of scoring higher than 12? Explain in detail how you found your answer using words, numbers, and/or pictures.

6P-7) Draw a spinner that fits all of these clues: There are five numbers on the spinner. Five is the greatest number. One of the numbers on the spinner comes up about 1/2 of the time. The number 3 comes up about 1/8th of the time. The number 2 comes up most often. The probabilities of 1,4, & 5 coming up are equal? Explain in detail how you found your answer using words, numbers, and/or pictures.

6P-4) Julio and Julia are playing a game with the dice. They roll both dice and them subtract the smaller number from the larger number. Julio gets 10 points for each answer that is an odd number and Julia gets 10 points for each answer that is an even number. Is this game fair? Why or why not? Explain in detail how you found your answer using words, numbers, and/or pictures.

6P-3) Fran wrote checks for her phone bill, gas bill, and electric bill. After she mailed her bills, she wasn't sure she put the right check in each envelope. What is the probability that exactly one check went to the right company? Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-8b) Strategy: Draw a picture C-623 and C-279 are Cyborgs, who work together on interstellar developments for the Cosmos Construction Company. Their last job was to clear a small rectangular area 200 feet wide and 600 feet long for a new dance club. They used a special planet planer, a bulldozer-type machine, to clear loose rocks and smooth the surface. The planet planer covers an area 20 feet across. If C-623 begins at a corner, and works his way into the center, on which trip around will he clear his half of the area? Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-6e) Strategy: Make a table or chart Marta made out the order for Jaguar Jeans. She ordered 7 pairs of jeans for every jacket, 1 shirt for every 2 pairs of jeans, 3 sweaters for every jacket, 2 pairs of shoes for each 3 sweaters, and 1 belt for every 3 jackets. If Marta ordered 36 jackets, how many items did she order altogether? Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-4d) Strategy: Look for a pattern The fierce army of ants marches forth to battle. The general makes up the whole first row. Two colonels make up the second row. Three lieutenant colonels form the third row. Four majors make up the fourth row. Five soldiers form the fifth row, and so on, row after row. If the army consists of 525 ants, how many rows are there, and how many are in the last row? Explain in detail how you found your answer using words, numbers, and/or pictures.