BHS CalcuSolve 2013

Good Morning and Welcome to the Brentwood 2013 CalcuSolve Competition! We hope you have a challenging and successful day! While we are waiting for all the teams to arrive, please: 1. Sit at the table to which you were assigned. 2. Make a nametag. Include your first and last name, school name, and team letter on the tag. Please wear the nametag during the entire competition. 3. Each person on your team should take one stapled packet of individual answer sheets and complete all the information on EVERY sheet. Print neatly! Your team letter is displayed on the sign at your table. Begin to practice for the competition by working on the Math Brain Warm-ups that are in your folder. We will go over the answers just before we begin the actual competition. If you need help or further direction, please find a Brentwood Ambassador or see Mrs. Anderson, Mrs. Hagerty, or Ms Greiner. Relax, Have Fun, and Good Luck! 2013 BHS CalcuSolve

Change, Please!- Answers 4 quarters 3 quarters, 1 dime, 3 nickels Warm Up Answers  360 degrees in a circle 640 acres in a square mile 1,000 milliliters in a liter 2, 000 pounds in a ton 5, 280 feet in a mile Change, Please!- Answers 4 quarters 3 quarters, 1 dime, 3 nickels 7 dimes, 6 nickels 1 half dollar, 2 quarters 3 quarters, 5 nickels 6 dimes, 5 nickels, 15 pennies 1 half dollar, 1 quarter, 2 dimes, 1 nickel 3 quarters, 2 dimes, 1 nickel 10 dimes OR 1 quarter, 6 dimes, 3 nickels 1 half dollar, 1 quarter, 1 dime, 1 nickel, 10 pennies Numeral- Initial Equations- Answers 1 voice in a solo 2 pints in a quart 3 teaspoons in a tablespoon 4 quarts in a gallon 5 toes on a foot 9 players on a baseball team 9 planets in the solar system 12 eggs in a dozen 16 tablespoons in a cup 36 inches in a yard 50 states in the United States 66 books in the Bible 88 keys on a piano 144 items in a gross 206 bones in your body 2013 BHS CalcuSolve

SCORING There will be seven Individual Questions. You will be given 5 minutes to earn 5 points for a correct answer on each Individual Question. OR You may wait for a clue, work an extra 2 minutes and earn 3 points for a correct answer on each Individual Question. There will be two Group Questions. Your team of students will be given 7 minutes to earn 10 points for a correct answer on each Group Question. 2013 BHS CalcuSolve

Group Question – Round #1 Mrs. Harrison is buying birthday gifts for her children. She buys some video games and some CDs from the Electronics Boutique. The CDs cost $22 less than the video games. She buys a total of 5 items and spends $109. Two of the items are video games. How much does she spend on all of the CDs? 2013 BHS CalcuSolve

Group Question – Round #1 Solution She spends $39 on the CDs. CDs $109 Video + $44 Games $109 - $44 = $65 $65 ÷ 5 = $13 = $13 $13 X 3 CDs = $39 2013 BHS CalcuSolve

Individual Question – Round #2 Question When a number is divided by 3, the remainder is 1. When the same number is divided by 4, the remainder is 2. If the number is between 50 and 60, what is the number? 2013 BHS CalcuSolve

Individual Question – Round #2 Clue The number is larger than 55. 2013 BHS CalcuSolve

Individual Question – Round #2 Solution The number is 58. Because the number has a remainder when divided by 3 or 4, it cannot be a multiple of 3 or 4. This eliminates: 51, 52, 54, 56, 57, Number Remainder when Divided by 3 Remainder when Divided by 4 53 2 1 55 58 59 3 2013 BHS CalcuSolve

Individual Question – Round #3 Question Farmer Brown has ducks and horses on his farm. These 29 animals have a total of 82 legs. How many horses does Farmer Brown have? 2013 BHS CalcuSolve

Individual Question – Round #3 Clue Farmer Brown has more ducks than horses. 2013 BHS CalcuSolve

Individual Question – Round #3 Solution Farmer Brown has 12 horses. Ducks Horses Animals Legs 20 (40 legs) 9 (36 legs) 29 76 19 (38 legs) 10 (40 legs) 78 18 (36 legs) 11 (44 legs) 80 17 (34 legs) 12 (48 legs) 82 2013 BHS CalcuSolve

Individual Question – Round #4 Question One day during lunch, Megan counts the number of students buying and packing a lunch at school. For every 5 students that buy a hot lunch, there are 2 students who pack their lunch. If she counts a total of 301 students, how many are buying a hot lunch? 2013 BHS CalcuSolve

Individual Question – Round #4 Clue More than 200 students purchase a hot lunch. 2013 BHS CalcuSolve

Individual Question – Round # 4 Solution 215 students purchase a hot lunch For every 7 students, 2 pack and 5 buy hot lunch In 301 students, there are 43 groups of 7 students 43 X 5 = 215 students buy hot lunch 2013 BHS CalcuSolve

Individual Question – Round # 5 Question Mandy has some marbles. When she gives half of her marbles to Dante, he has 3 times as many as her. When she gives half of her remaining marbles to Julian, he has four times as many as her. If Julian now has 100 marbles, how many did Dante start with? 2013 BHS CalcuSolve

Individual Question – Round # 5 Clue After Mandy gave Dante and Julian her marbles, she had 25 left. 2013 BHS CalcuSolve

Individual Question – Round # 5 Solution Dante started with 100 marbles. Mandy 1. 3. Julian has 4 times as many marbles as Mandy; Mandy has 25. 4. Dante has 150 marbles now. He received 50 from Mandy, so he started with Dante 100 marbles. 2. We know Julian has 100 Julian marbles, so each small box represents 25 marbles. 2013 BHS CalcuSolve

Individual Question – Round # 6 Question My mother bought a painting at a yard sale that measures 25” by 15”. She wants to put a frame all around the painting that is 3” wide. What is the area of the painting, including the border? 2013 BHS CalcuSolve

Individual Question – Round # 6 Clue The border will increase the length of the painting by 6 inches. 2013 BHS CalcuSolve

Individual Question – Round # 6 Solution The area of the painting, including the border, is 651 square inches. The border will increase each side by 6” (3” on either side) 31” x 21” = 651 square inches or in2 21” 31” 15” 25” 3” 2013 BHS CalcuSolve

Individual Question – Round # 7 Question Ryan’s dad is 3 times as old as Ryan. Ryan’s brother Josh is 5 years older than Ryan. If you add all three of their ages together, you will get 80. How old is Ryan’s brother? 2013 BHS CalcuSolve

Individual Question – Round # 7 Clue Ryan’s dad is older than 40. 2013 BHS CalcuSolve

Individual Question – Round # 7 Solution Ryan’s brother Josh is 20 years old. Josh = Ryan’s age + 5 years Dad = Ryan’s age x 3 J = R +5 D = R x 3 or 3R R + J + D = 80 years R + (R + 5) + (3R) = 80 years 5R + 5 = 80 years 5R = 75 years R = 15 years J = R + 5 J = 15 + 5 J = 20 years 2013 BHS CalcuSolve

Individual Question – Round # 8 Question In the following problems, the letters A through E each represent a different digit 0 – 9. What is the value of the letter B? D + E = AB D x E = CB D – E = E D ÷ E = B 2013 BHS CalcuSolve

Individual Question – Round # 8 Clue 2013 BHS CalcuSolve

Individual Question – Round # 8 Solution B = 2 D + E = AB D x E = CB D – E = E D ÷ E = B Because D – E = E, we know that D must be a double of E. There are only 3 sets of numbers that will fit the criteria of the problem: 8 & 4, 6 & 3, 4 & 2. D + E must equal a 2 digit number that starts with 1, so that eliminates all sets but 8 & 4. 8 + 4 = 12 8 x 4 = 32 8 – 4 = 4 8 ÷ 4 = 2 A = 1; B = 2; C = 3; D = 8; E = 4 2013 BHS CalcuSolve

Group Question – Round # 9 Question Luke rolls three dice numbered from 1-12. What is the probability he will roll a number that is a multiple of 3 AND a factor of 12 on each die if he rolls all 3 at once? Express your answer as a fraction in simplest form. 2013 BHS CalcuSolve

Group Question – Round # 9 Solution 1/64 All possible outcomes from one di: 1 2 3 4 5 6 7 8 9 10 11 12 Multiples of 3: 3, 6, 9, 12 Factors of 12: 1, 2, 3, 4, 6, 12 Multiple of 3 AND factor of 12: Probability of rolling one of the bolded numbers on 1 die: 3/12, which simplifies to ¼ Probability of rolling a 3, 6, or 12 on all three dice: ¼ x ¼ X ¼ = 1/64 2013 BHS CalcuSolve