1. 2008 Florida MATHCOUNTS Ciphering Questions

2. A co-worker clicks his pen 30 times every minute. During an hour long meeting, how many times does he click his pen?

3. Answer 1 800 30 cl/min × 60 min = 1 800 cl

4. How many triangles are in the figure below?

5. 1 Answer 8 3 4 2 7 6 8 5

6. Paul lists his house to sell for $280 000. Jane offers to buy it for $238 000. What is the percentage of discount represented by Jane’s offer?

7. Answer 15 (%) Discount = Original – Sale Price = $280 000 − $238 000 = $42 000 42 000/280 000 = (3 ×14)/(20×14) = 15 %

8. Solve for x: 3x − 13 = 11 − x

9. Answer 6 3x− 13 = 11 −x 4x = 24

10. Tess rides her bicycle to school at a rate of 10 mi/h. Tarryn walks to school at a rate of 3 mi/h. Tess lives 5 mi and Tarryn lives 2 mi from school. How many minutes longer does Tarryn require to get to school?

11. Answer • (min) • Tess: 5mi/(10mi/h)=1/2h=30min • Tarryn:2mi/(3mi/h)=2/3h=40min

12. If a circle is divided into eight equal sectors, what is the degree measure of the central angle of any one sector?

13. Answer 45 (degrees) 360/8 = 45

14. Evaluate √x2 for x = 42− 52

15. Answer 9 √x2 = |x|. Here x = 42− 52 = 16− 25 = −9 and |−9| = 9.

16. The price of a certain television is discounted 10 %, and the reduced price is then discounted 10 %. This sequence of discounts is equivalent to a single discount of what percent?

17. Answer 19 (%) 10 % off means a cost of 90 % for a cost factor of 0.9. Applying twice yields 0.9 × 0.9 = 0.81 = 81 % price for 100 % − 81 % = 19 % discount.

18. Evaluate: 2 × 6! + 4 × 5! + 3 × 4! + 8 × 2!

19. Answer 2 008 2! = 2; 4! = 4×3×2! = 24; 5! = 5×4! =120; 6! = 6×5! = 720. 2 × 720 + 4 × 120 + 3 × 24 + 8 × 2 = 1 440 + 480 + 72 + 16 = 2 008.

20. The sides of a special small prototype aircraft wing have lengths in the ratio 3:5:7. The perimeter of the wing is 90 cm. How many millimeters long is the longest side?

21. Answer 420 (mm) Long side is 7/(3 + 5 + 7) of the total perimeter. Long side = (7/15) × 90 cm = 42 cm = 42 cm × 10 mm/cm = 420 mm.

22. A worker was paid $5/h to move concrete blocks. In the first hour he moved 75; in the second hour he moved 50; in the third hour he moved 25. How many cents on average did it cost to move each block?

23. Answer 10 (¢) (3 h × $5/h) / (75+50+25) blk = $15 / 150 blk = $0.10/blk = 10 ¢/blk.

24. Solve for x: (24)(103) = 400x

25. Answer 40 x = (24)(103) / 400 =2×2×2×2×10×10×10/400

26. Surveyors once used a “chain” for measurement. A chain was 66 ft long. An acre has an area of 10 square chains. How many square feet are there in 10 acres?

27. Answer 435 600 (ft2) 662 = 62× 112 = (36 × 11) × 11

28. Bill drives north at 40 mi/h and Jeff drives east at 30 mi/h. They meet after 24 min of driving. How many miles apart were they when they started driving?

29. Answer 20 (mi) 30 mi/h × 24 min × h/60 min = 12 mi 40 mi/h × 24 min × h/60 min = 16 mi 3-4-5 right triangle with scale factor of 4 mi. 2 5

30. Five times the smallest of three consecutive even integers is six more than the product of four and the largest of the even integers. What is the value of the largest of the even integers?

31. Answer 26 Numbers are n− 4,n− 2, n. 5(n− 4) = 6 + 4n. 5n− 20 = 4n + 6. n = 26.

32. A cow produces 40 lb of phosphorus per year. How many tons of phosphorus per year are generated by a herd of 100 cows?

33. Answer 2 (tons) 100 cow × (40 lb/yr)/cow × 1 yr = 4 000 lb × ton/2 000 lb = 2 ton

34. How many minutes does it take to travel 120 miles at 400 miles per hour?

35. Answer 18 (min) 120 mi / (400 mi/h) = 0.3 h = 0.3 h × 60 min/h = 18 min.

36. Andrea has a bag of candy with 8 red, 12 blue, 4 yellow, and 16 green candies. What is the percentage of yellow candies in the bag?

37. Answer 10 (%) 4 / (8 + 12 + 4 + 16) ×100 %

38. An elementary school has a prism-shaped water tower that is 20 ft wide, 20 ft long, and 10 ft deep. Each of the school’s 40 students requires 25 ft3 of water per day. How many days will the water in one full tower last without refill?

39. Answer 4 (d) 20 ft × 20 ft × 10 ft 40 st × 25 ft3/(st · d)

40. The Smiths are planning to remodel their kitchen floor that measures 9 ft by 12 ft by using square tiles that are 18 in. on each side. Assuming the tiles abut edge to edge, how many tiles will the Smiths need?

41. Answer 48 (tiles) tile = 18 in × 1 ft / 12 in = 3/2 ft. l =12ft/(3/2ft/ti)=12×2/3 ti = 8ti. w = 9×2/3 ti = 6ti. Area = lw = 8 × 6 tiles

42. A contractor must place 150 ft of guardrail adjacent to one end of a bridge. The standard connection section at the bridge is 10 ft and the other end-section has to be 40 ft. If a standard guardrail panel is 12.5 ft, how many panels are needed for the remaining section?

43. Answer 8 (panels) Length of remaining section is 150 ft − (10 ft + 40 ft) = 100 ft. 100 ft /12.5 ft = 8.

44. A 10 ft × 20 ft concrete slab is being replaced. It will be connected to adjacent slabs on all sides by dowel bars. If the dowel bars are placed 5 ft apart, but at least 2.5 ft from the corners, how many dowel bars are needed to go around the perimeter?

45. Answer 12 (dowel bars) On each 10 ft side at 2.5 ft, 7.5 ft for 2 dowels; on each 20 ft side at 2.5 ft, 7.5 ft, 12.5 ft, and 17.5 ft for 4 dowels Two of each side length, so 2(2 + 4).

46. A Tallahassee skyscraper will be 25 stories tall and have a trapezoidal foundation of area 10 000 ft2. If the building sits on a city block 50 yd × 60 yd, how many square feet remain in the block that could be available for pedestrians and landscaping?

47. Answer 17 000 (ft2) 50yd×60yd×(3ft/yd)2 −10 000ft2 = (3 000×9 −10 000)ft2 (Building height and foundation shape are irrelevant.)

48. Annual costs for a rental property are: Taxes of $6000, Insurance of $4500, and Utilities of $1500. Assuming no other costs, how much does the unit need to be rented for each month to break even?

49. Answer 1 000 ($/mo) $6 000 + $4 500 + $1 500 = $12 000 $12 000 / 12 month = $1 000/month

50. During a hat sale, all hats were marked down 75 %. Kathy bought a hat with an original price of $5.00. How many dollars did Kathy save by buying the hat on sale?