Grade Seven AnswersGrade Seven AnswersAnswer:
Let D = the weight of one duck d = the weight of one duckling Solve: (3D + 2d = 32)*3 ------> 9D + 6d = 96 (4D + 3d = 44)*2 ------> 8D + 6d = 88 ______________ 1D + 0d = 8 -----> D = 8 Substitute to solve for d: 4D + 3d = 44 4(8) + 3d = 44 32 + 3d = 44 3d = 12 d = 4 Thus, 2D + d = 2(8) + 4 = 20 kgs.
Answer:
Let x = rate of one man = 23 m3/ 1 day = 8m3/day 3x = rate of three men = 3(8m3/day) = 24m3/day Volume to be shoveled = 64m3 Therefore, it would take three men 64m3/(24m3/day) = 2 2/3 days
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Let x = total number of bags 5(1/2 x) + 2 (1/2 x) = 252 2.5x + 1x = 252 3.5x = 252 x = 72 bags.
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Let x = number of seats in Theatre 3 T1 = Theatre 1 = 270 seats T2 = Theatre 2 = 150 + x T1 + T2 + T3 = 800 seats 270 + (150 + x) + x = 800 420 + 2x = 800 x = 190 If there are x = 190 seats in theatre 3, then Theatre 2 has 150 + 190 = 340 seats
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If the price of 5 Kg of flour in 1969 = $0.75, then 1970 = $0.75 x 1.15 = $0.8625 1971 = ($0.75 x 1.15) x .95 = $0.82
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l x h x w = 60 h(5)(4) = 60 h = 3 A(1) = 4 x 5 = 20 2A(2) = 2(3)(5) = 30 2A(3) = 2(3)(4) = 24 4A(4) = 4(3)(3) = 36 Total A = A(1) + 2A(2) + 2A(3) + 4A(4) = 20 + 30 + 24 + 36 = 110cm2
Answer:
Let x = price of lipstick Let 1/2 x = price of shampoo Cost of lipstick AND shampoo, combined = x + 1/2 x Money spent on lipstick AND shampoo combined: $50.00 - ($15.00)*2 = $20.00 Therefore, x + 1/2 x = $20.00 1.5x = $20.00 x = $13.33 Lipstick cost: x = $13.33 Shampoo cost: 1/2 x = 1/2 * $13.33 = $6.67
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Let x = Stephanie's contribution. $30.00 + $10.00 = $40.00 $40.00 + x = $54.99 x = $14.99
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e = 3(3)-1 = 8 f = 1/2(3) = 1.5 g = 3/8(3) + (3/8)(3) = 18/8 = 2.25 Volume (1) = 1/2(a)(c)(b) Volume (2) = 1/2(a)(c)(f) = 1/2(3)(4)(3) = 1/2(3)(4)(1.5) = 36/2 = 18litres = 9 litres = (18)dm3 = (9)dm3 Volume (3) = (e)(g)(c) = (8)(2.25)(4) = 72 litres = (72)dm3 Total Volume = 18 + 9 + 72 = 99 litres = (99)dm3 Let t = time t = 99 x 1min/2l x 60sec/1min = 99 (60sec)/2l = 49.5(60sec) = 2970
Answer:
Dimensions B: 5/8 = 8/x 64 = 5x 12.8 = x (a) Surface Area = 2 * Area A + 2 * Area B + Area (top) + Area (bottom) = 2(8*5) + 2(8*12.8) + 2(5*12.8) = 412.8 (b) Volume = l x w x h = (12.8)(5)(8) = 512
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2r + 3L + 3w + 3pi*a = 2(10) + 3(100) + 3(20) + 3pi(20) = 568.50m (2r+L) + 2L + 3W + 3piW = (2(10)+40) + 2(40) + 3(20) 3pi(20) = 388.50 m
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75% full = 75% * 1000 horses = 750 horses If there are 200 ponies, there must be (750 - 200) = 550 quarter horses
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Let x = width of chalkboard Therefore, 3x = length of chalkboard Since sides of square are equal, 3x - 3 = x + 3 2x = 6 x = 3 Dimensions of chalkboard: width = x = 3 meters wide length = 3x = 9 meters long
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3 x 152km/month x 12 months/year = 5472 km/year.
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(700.00)(5/6)(4/5) = $466.67
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4 triangles
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a) 225 * 8 litres + 515 * 27 litres = Total Volume 15705 litres = 15.705 kilolitres b) [(150*8 + 5*27) / 15705] x 100 percent = 8.500 percent.
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Cost of first kilometer = $0.30 Total cost of additional kilometers = (3.20 - 0.30) = 2.90 Total number of kilometers = 1 + ($2.90/$0.05) = 1 + 58 = 59 km
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SHAWN RACHEL start 0.05 litres = 0.05 0.05 litres = 0.05 moving 8km * (1L/22km) = 0.36 9km * (1L/20km) = 0.45 stopped 2min * (0.16L/min) = 0.32 0 = 0 ____ ____ TOTAL 0.73 L 0.50 L Therefore, Shawn used more gas
Answer:
Total area of square = (1/4 + 3/4) * (2/3 + 1/3) = 1 * 1 = 1 Shaded area = (2/3 * 3/4) = 0.5 Fraction of Total area shaded = 0.5/1 = 50%
Answer:
Let x = the number of hours that had already passed 1/4 x = the number of hours remaining IF total number of hours in a day = 40, THEN x + 1/4x = 40 5/4x = 40 160x = 5 x = 160/5 x = 32 Hours remaining = 1/4 x = 1/4(32) = 8
Answer:
Volume = l * w * h = (20)(30)(40)cm3 = 24000cm3 New height = initial h + 0.3h = 1.3h = 1.3 * 40cm = 52 cm IF height = 52 cm, solve for w: Volume = l * w * h 24000 cm3 = (20cm)(w)(52cm) 24000 cm3 = 1040(w)cm2 w = 23.08 cm
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Pattern: 16 - 13 = 3 10 - 7 = 3 10 - 9 = 1 8 - 7 = 1 3 barks for 1 car Therefore, 22 barks for 12 cars.
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Answer:
Let x = price for each big rig tire Size Price/tire 0.75m $100/4 = $25.00 each 1.5m x Solve for x: 0.75m/$25.00 = 1.5/x 0.75x = 1.5 * $25.00 0.75x = $37.50 x = $50.00/tire Therefore: Price for 18 tires = 18($50.00) = $900.00
Answer:
1)Cost of Pizza = $20.00 PROPORTIONS: Jane: 5/20 = 1/4 Mike: 8/20 = 4/10 = 2/5 Mary: 3/20 Joe: 4/20 = 1/5 2)
Jane: 5/20 = 1/4 Mike: 8/20-4/20 = 4/20 = 1/5 Mary: 3/20 + 4/20 = 7/20 Joe: 4/20 = 1/5
Answer:
Let x = the number of cookies eaten on the first day Cookies Eaten Day 1 x 2 x + 1(6) 3 x + 2(6) 4 x + 3(6) 5 x + 4(6) TOTAL 5x + 10(6) = 100 cookies Solve for x: 5x + 10(6) = 100 5x + 60 = 100 5x = 40 x = 8
Answer:
Since s = sides of square Area square = s^2 Area triangle = (1/2)b*h = (1/2)(1/2 s)(1/2 s) = 1/8 s^2 Ratio = Area triangle/Area square = 1/8
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Time to connect two chains = 1 cut + 1 weld = 10s + 25s To connect all chains together = 5 connections = 5(10+25)s = 5(35) = 175
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Let x = artist's scale 1) Convert meters (m) to centimeters (cm) In reality, rose bush = .75m * 100 cm/m = 750 cm 2) Solve for x 1.5x = 750 x = 750/1.5 x = 500 cm IF artist's scale = 1 cm:500cm THEN In reality, house = 7.5cm * 500 cm = 3750 cm = 3.75 m
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When 3 lines are extended from vertex, opposite side is divided into four sections When 3 lines are extended from two vertices: Number of nonoverlapping sections formed = 42 = 16 If 4 lines are extended from vertex, opposite side is divided into five sections Therefore, when 4 lines are extended from two vertices: Number of nonoverlapping sections formed = 52 = 25
Answer:
Let x = total number of points for the season 1653 points were scored by ST. F.X., but ST. F.X. had only 38 percent of the total points for all four teams. Solve for x: x= 1653/0.38 = 4350 points ACADIA: 14% * 4350 = 609 DALHOUSIE: Acadia + 50 = 609 + 50 = 659 SMU: 4350 - (1653 + 609 + 659) = 1429
Answer:
Total area of quadrilateral = x * y A1 = A2 = A3 = A4 Solve: A1 = 1/2 (b * h) b = 1/2 x h = 1/2 y = 1/2 (1/2 x * 1/2 y) = 1/8 xy Since A1 = A2 = A3, A1 + A2 + A3 = 1/8 xy + 1/8 xy + 1/8 xy = 3/8 xy Since total area of quadrilateral = x * y = xy, 3/8 of total area of quadrilateral is shaded by triangles A1, A2, and A3
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Rachel: WEEKLY: $5.15/hr * 13 hrs/wk = $66.95/wk YEARLY: $66.95/wk * 52 weeks = $3481.40/yr Stephanie: WEEKLY: $5.15/hr * 20 hrs/wk = $103/wk YEARLY: $103 * 52 weeks = $5356/yr IF Stephanie and Rachel make the same amount of money in one year, THEN Stephanie must only work: ($3481.40/yr)/($103/wk) = 33.8 weeks Therefore, she must take 52 - 33.8 = 18.2 weeks/yr Unpaid Vacation Time
Answer:
a)p = 2(6 + 210) + 2(6+460) = 432 + 932 = 1364m b)
Area of paved path = 2*3*466 + 2*3*210
= 4056 m2
Answer:
Let x = amount covered DAY Amount Covered 16 x 15 1/2 x 14 1/4 x Therefore, on Day 14, 1/4 of the petri dish was covered with bacteria
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Amount of change Joe receives: $2.00 - $1.08 = $0.92 Two possible variations of coins received: (i) 3 quarters, 3 nickels, 2 pennies 3(.25) + 3(.05) + 2(.01) = .92 (ii) 2 quarters, 4 dimes, 2 pennies 2(.25) + 4(.10) + 2(0.01) = .92
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Equation for y1: y1 = m1 x + b m1 = (12-0)/(9-0) = 4/3 y1 = 4/3 x + b Since y1 passes through origin, 0 = b y1 = 4/3 x + 0 y1 = 4/3 x Equation for y2: y2 = m2 x + b m2 = (0-12)/(16-0) = -3/4 y2 = -3/4 x + b y2 passes crosses y-axis at (0,12), therefore b = 12 y2 = -3/4 x + 12 Since m1 = negative reciprocal of m2, y1 is perpendicular to y2
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Water lost per second: 3 * (1 1/3 mL) = 4mL Number of seconds in one year: 60s/min x 60 min/hr x 24hr/day x 365d/y = 31 536 000 s Water lost in one year = 4mL/s * 31 536 000 s = 126 144 000 mL Convert to Litres: 126 144 000mL * 1L/1000 mL = 126 144 litres
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Area of circle = pi * r2 Side of square = 2 * r = 2r Area of square = (2r)2 = 4r2 Area of shaded region = Area of square - 4 * (1/4 area of each circle) = 4r2 - 4 * 1/4(pi * r2) = 4r2 - pi r2 = (4 - pi)r2
Answer:
PURCHASE PRICE: Rachel: 5/6 * $5600.00 = $4666.67 Raelene: 4/5 * $4666.67 = $3733.33 Rick: 3/4 * $3733.33 = $2800.00 OR you can take a shortcut: Rick paid: $5600.00 (5/6)(4/5)(3/4) = $2800.00
Answer:
Travel time from A to C = 12:45 -11:00 = 1 hr 45 min = 1.75 hr Distance travelled: D = Rate * Time = 3 km/hr * 1.75 hr = 5.25 km Distance remaining (from point C to B): = (12 - 5.25) km = 6.75km Time remaining = 2:00 - 12:45 = 1 hr 15 min = 1.25 hr Rate at which distance must be travelled: Rate = Distance/Time = 6.75 km / 1.25 hr = 5.4 km/hr
Answer:
AO = BO = CO = DO = EO = 5 Therefore, we have 5 isosceles triangles. The altitude of an isosceles triangle intersects the side with which it makes the 90 degree angle.h of each triangle = square root of 5^2-3^2 = 4.05 Aera = 5 (1/2)(4.05)(5.88) = 59.54
Answer:
Area of semicircle = 1/2 pi r2 r = 3 Area of Trapezoid = 1/2(AD)(AB+CD) Total Area = 1/2 pi (9) + 1/2(6)(12+8) = 74.137 cm2
Answer:
360 degrees = 120 degrees + 90 degrees + C + (2/3 * C) 360 = 210 + 5/3 * C 150 = 5/3C 450 = 5C 450/5 = C 90 = C Substitute: If C = 90 degrees, Then D = 2/3 * 90 = 60 degrees
Answer:
The four sides of EFGH are equal Find length of one side: To find HG: (HC)2 + (CG)2 = (HG)2 Square root (32 + 12) = HG Square root (10) = HG Since four sides are equal, Area of EFGH = (square root 10)2 = 10
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Each revolution of B meets 24 teeth of A Therefore, (36 - 24) = 12 teeth of wheel A are not met with the first revolution of B Since 12/24 = 1/2 Wheel B must turn 1 1/2 times for every revolution of A
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Triangle BAC similar Triangle EFC Triangle DCA similar Triangle EFA Therefore, 30/h = 40/(40 - b) 20/h = 40/b 1200 - 30b = 40h Substitute 1200 - 30b = 20b <-------------------- 40h = 20b 1200 - 30b = 20b h = 1/2 b 1200 = 50b 1200/50 = b Substitute 24m = b ---------------------> h = 1/2 (24m) h = 12 m
