2008 FloridaMATHCOUNTS

Ciphering Questions

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

Answer

1 800

30 cl/min × 60 min = 1 800 cl

How many triangles are in the figure below?

Answer

8

1

23 4

5

6 7

8

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?

Answer

15 (%)

Discount = Original – Sale Price = $280 000 − $238 000 = $42 000

42 000 / 280 000 = (3 × 14)/(20 × 14) = 15 %

Solve for x:

3x − 13 = 11 − x

Answer

6

3x − 13 = 11 − x 4x = 24

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?

Answer

10 (min)

Tess: 5 mi/(10 mi/h) = 1/2 h = 30 min

Tarryn: 2 mi/(3 mi/h) = 2/3 h = 40 min

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

Answer

45 (degrees)

360/ 8 = 45

Evaluate

√ x2 for x = 42 − 52

Answer

9

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

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?

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.

Evaluate:

2 × 6! + 4 × 5! + 3 × 4! + 8 × 2!

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.

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?

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.

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?

Answer

10 (¢)

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

Solve for x:

(24)(103) = 400x

Answer

40

x = (24)(103) / 400 = 2 × 2 × 2 × 2 × 10 × 10 × 10 / 400

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?

Answer

435 600 (ft2)

662 = 62 × 112 = (36 × 11) × 11

22

22

ft 66100

ch 1ft 66

ac 1ch 10

ac 10

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?

Answer

20 (mi)

30 mi/h × 24 min × h/60 min = 12 mi40 mi/h × 24 min × h/60 min = 16 mi

3-4-5 right triangle with scale factor of 4 mi.

2 5

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?

Answer

26

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

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

Answer

2 (tons)

100 cow × (40 lb/yr)/cow × 1 yr= 4 000 lb × ton/2 000 lb = 2 ton

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

Answer

18 (min)

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

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?

Answer

10 (%)

4 / (8 + 12 + 4 + 16) × 100 %

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?

Answer

4 (d)

20 ft × 20 ft × 10 ft

40 st × 25 ft3/(st · d)

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?

Answer

48 (tiles)

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

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?

Answer

8 (panels)

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

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?

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 dowelsTwo of each side length, so 2(2 + 4).

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?

Answer

17 000 (ft2)

50 yd × 60 yd × (3 ft/yd)2 − 10 000 ft2

= (3 000 × 9 − 10 000) ft2

(Building height and foundation shape are irrelevant.)

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?

Answer

1 000 ($/mo)

$6 000 + $4 500 + $1 500 = $12 000

$12 000 / 12 month = $1 000/month

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?

Answer

($) 3.75

$5.00 × 75/100 = $5.00 × 3/4 =

$15.00 / 4 = $3.75

A pile of dirt is loaded onto a truck that holds 10 cubic yards and the truck is exactly half full. How many cubic feet of dirt has been loaded into the truck?

Answer

135 (ft3)

½ × 10 yd3 × (3 ft/yd)3

= 5 × 27 ft3 = 135 ft3

Sam uses a bucket that holds 31 lb to empty a pool of water shaped as a 10 ft × 10 ft × 10 ft rectangular prism. If water weighs 62 lb/ft3, how many bucket loads will Sam have to lift, assuming he fills the bucket every load?

Answer

2 000 (bucket loads)

(10 ft)(10 ft)(10 ft)(62 lb/ft3) / (31 lb/ld) = 1 000 × 2 ld

2

A skateboard half-pipe 900 ft long needs to be painted. If the radius is 10 ft, how many square yards of surface need to be painted? For π, use 3.14.

Answer

3 140 (yd2)

Half cylinder lateral surface area = ½(2πrh). r = 10 ft, h = 900 ft, yd2 = (3 ft)2 = 9 ft2

3.14 × 10 ft × 900 ft /(9 ft2/yd2)

A digital camera memory card has a 10 Mb capacity. If the camera is set to take JPEG pictures each requiring 50 kb of memory, how many pictures can the card hold?

Answer

200 (pictures)

10 Mb / (50 kb/pict) = 10 000 000 b / (50 000 b/pict) = 200 pict

A string, supposedly of length 0.100 mi, has to be measured to confirm its length. If Christopher measures the string with a yard-stick and the claimed length is correct, how many yards long will he find the string to be?

Answer

176 (yd)

5 280 ft/mi × 0.1 mi = 528 ft.528 ft × (1 yd / 3 ft) = 176 yd.

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