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Problem Solving

Problem Solving. Ms. Crusenberry 8-2013. Whole numbers. Chilhowie High School has 935 twelfth-grade students, 862 eleventh-grade students, and 1,036 tenth-grade students. What is the school’s total enrollment?

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Problem Solving

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  1. Problem Solving Ms. Crusenberry 8-2013

  2. Whole numbers • Chilhowie High School has 935 twelfth-grade students, 862 eleventh-grade students, and 1,036 tenth-grade students. What is the school’s total enrollment? • Your test grades during the first quarter are 75, 80, 92, 100, 83, 60 and 85. What is your test grade total for the first quarter? • You bowl nine games. Your scores are 238, 93, 179, 217, 64, 278, 108, 76 and 240. What is your pin total?

  3. Answers • 935 + 862 + 1036 = 2833 • 75 + 80 + 92 + 100 + 83 + 60 + 85 = 575 • 238 + 93 + 179 + 217 + 64 + 278 + 108 + 76 + 240 = 1493

  4. continued • You weighed 136 pounds on Monday. At the end of two weeks of exercising, you weighed 128 pounds. How much weight did you lose? • During inventory, you find that of the 2,482 books on the shelves, 482 are biographies, 726 are art books, and 534 are mysteries. The rest are fiction stories. How many books are fiction stories? • You save $13 a week. There are 52 weeks in a year. How much will you save in one year?

  5. Answers • 136 – 128 = 8 • 2482 – (482 + 726 + 534) = 740 • 13 x 52 = 676

  6. continued • Each package of school duplicating paper contains 500 sheets of paper. How many sheets of paper are contained in 17 packages of paper? • Your cat has five kittens. Each kitten eats 3 ounces of kitten food per day. How many ounces of food do the five kittens eat in 7 days? • You have a job after school. You earned $868 over a 14 week period. What is your average weekly salary?

  7. Answers • 500 x 17 = 8500 • 3 x 5 = 15 ounces x 7 = 105 ounces • 868 ÷ 14 = 62

  8. continued • Thumbtacks are sold on cards of 48 tacks each. How many cards must be bought if you need 1,104 tacks? • Your new car averages 25 miles per gallon. How many gallons will you need to drive 455 miles? • You paid $816 for heat last year. How much did you pay each month? • Your first-quarter grades are 85, 68, 90 and 75. What is the average? • Your grades in night school are 93, 72, 85, 81 and 73. What is your average?

  9. Answers • 1104 ÷ 48 = 23 • 455 ÷ 25 = 18.2 • 816 ÷ 12 = 68 • (85 + 68 + 90 + 75)/4 = 79.5 • (93 + 72 + 85 + 81 + 73)/5 = 80.8

  10. Fractions • You want to build 5 shelves, each measuring 3 ¾ feet long. How many feet of shelving board will you need? • If it takes 2 ¼ cups of flour to make a cake, then how much flour will you need to make ½ of the recipe? • You want to fence your property. Each side of his square lot is 14 ½ feet long. How much fencing do you need?

  11. Answers • 3 ¾ x 5 = 15/4 x 5/1 = 75/4 = 18 ¾ • 9/4 ÷ 2/1 = 9/4 x ½ = 9/8 = 1 1/8 • 14 ½ x 4 = 29/2 x 4/1 = 116/2 = 58

  12. continued • A group of home economics students needs to divide ¾ pound of sugar 3 ways. What fraction of a pound will each student get? • How many pieces of pipe can be cut from a 12 foot piece of pipe if each is to be 2/3 of a foot long? • A mathematics class makes a giant turkey sandwich that measures 7 ½ feet long. If 15 students share the sandwich equally, how long is each student’s serving? • You are a plumber and you join two pieces of pipe. They measure 7 3/16” and 4 7/16”. How long is the new piece of pipe?

  13. Answers • ¾ ÷ 3/1 = ¾ x 1/3 = 3/12 = ¼ • 12 ÷ 2/3 = 12/1 x 3/2 = 36/ 2 = 18 • 7 ½ ÷ 15= 15/2 ÷ 15/1 = 15/2 x 1/15 = 15/30 = ½ • 7 3/16 + 4 7/16 = 11 10/16 = 11 5/8

  14. continued • Miss Watts is building a bookshelf. She needs a piece of wood measuring 3 ½ feet long and a piece of wood 5 ¼ feet long. What is the total length of the wood she needs? • If 2 3/8 yards of fabric on a bolt are irregular and the bolt contains 6 1/3 yards of fabric, then how much regular fabric remains?

  15. Answers • 3 ½ + 5 /14 = 7/2 + 21/4 = 14/4 + 21/4 = 35/4 = 8 ¾ • 6 1/3 – 2 3/8 = 19/3 – 19/8 = 152/24 – 57/24 = 95/24 = 3 23/24

  16. Decimals • The average lap speed in the Oceanside 500 auto race is 352.627 km/h. round to the nearest tenth. • A centimeter is about .3937 inches. Round this to the nearest hundredth. • One rainy week, it rains 2.5 inches on Monday, 1.63 inches on Tuesday, and 3 inches on Wednesday. What is the total rainfall for these three days? • You buy potatoes for $2.98, tomatoes for $1.53, steak for $5.65, and a peach pie for $2.50. What is your change from $20.00?

  17. answers • 352.627 km/h = 352.6 • .3937 = .39 • 2.5 + 1.63 + 3 = 7.13 • 2.98 + 1.53 + 5.65 + 2.5 = 12.66 then 20.00 – 12.66 = 7.34

  18. continued • What is the total length of 6 pieces of ribbon each .012 foot long? • What is the total distance traveled at 1.3 mph for .6 hour? • What is the cost of .6 pound of grapes at $.93 per pound? • You have to cut a 2.3 foot long pipe into 4 equal pieces. How long is each piece? • If three dozen pencils cost $6.48, then what does one pencil cost?

  19. Answers • 6 x .012 = 0.072 • 1.3 x .6 = .78 • .6 x .93 = .558 • 2.3 ÷ 4 = .575 • 6.48 ÷ 36 = .18

  20. continued • Your part time job pays $118.65. how many hours do you work if you earn $5.65 per hour? • At $.33 per pound, how many pounds of potatoes can you buy for $2.64? • We drove a distance of 885 miles on our vacation. The total driving time was 20 hours. What was the average driving speed to the nearest hundredth? • A machinist measures four blocks of metal and gets these readings: 1.96 inches, 1.93 inches, 2.01 inches, and 1.94 inches. What is the average reading?

  21. Answers • 118.65 ÷ 5.65 = 21 • 2.64 ÷ .33 = 8 • 885 ÷ 20 = 44.25 • (1.96 + 1.93 + 2.01 + 1.94)/4 = 1.96

  22. Ratio & proportion • Apple Green paint is made by mixing 7 parts yellow to 3 parts blue. How much yellow should be mixed with 9 pints of blue? • Purple paint is 5 parts blue to 1 part red. How much red should be mixed with 2 quarts of blue? • Mix 3 quarts of water with 2 lemons to make lemonade. How many quarts of water are mixed with 1 lemon?

  23. Answers SET UP AS PROPORTIONS • 7/3 = x/9 yellow/blue 3x = 63x = 21 • 5/1 = 2/x blue/red5x = 2x = .4 • 3/2 = x/1 water/lemons2x = 3x = 1.5 or 1 ½

  24. continued • A car travels 240 miles on 15 gallons of gas. How far can the car travel on 20 gallons of gas? • You can drive 250 miles in 4 hours. How far can you drive in 6 hours? • Oranges are selling at the rate of 12 oranges for a dollar. How much will 27 oranges cost?

  25. Answers SET UP AS PROPORTIONS • 240/15 = x/20 miles/gallons4800 = 15x320 = x • 250/4 = x/6 miles/hours1500 = 4x375 = x • 12/1 = 27/x oranges/dollars27 = 12x2.25 = x

  26. Review • Write each ratio as a fraction in simplest form” a. 18 to 24 b. 48 to 32 • Write a ratio to compare these amounts: a. 35 minutes to 1 hour b. 15¢ to 25 ¢ • Tell whether or not each pair of ratios forms a proportion. Use = or = a. 12/15 _____ 8/10 b. 12/8 _____ 4/3

  27. Review • Solve for the missing number: a. n/8 = 6/12 b. 4/10 = n/15

  28. Answers 1a. 18/24 = 34 1b. 48/32 = 6/4 = 3/2 = 1 ½ 2a. 35:1 2b. 15:25 = 3:5 3a. 12/15 __=___ 8/10 12 x 10 = 120 8 x 15 = 1203b. 12/8 __ = __4/3 12 x 3 = 36 8 x 4 = 32 4a. n/8 = 6/12 4b 4/10 = n/15 12n = 48 10n = 60 n = 4 n = 6

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